Maths-
General
Easy

Question

What expression represents the total area of the four white triangles?

Hint:

The methods used to find the product of binomials are called special products.
Multiplying a number by itself is often called squaring.
For example (x + 3)(x + 3) = (x + 3)2
Area of a square = (side)2

The correct answer is: 12x + 36


    The area of the outer square of side x+6 cm = (x+6)2

    (x+6)2  = (x+6)(x+6) = x(x+6) +6(x+6)

    = x(x) + x(6) +6(x) +6(6)

    = x2 + 6x + 6x + 36

    = x2 + 12x + 36
    The area of the inner square of side x cm = x2
    Now, Total area of four white triangles = Area of the outer square - area of the inner square

    = x2 + 12x + 36 - x2

    = 12x + 36
    Final Answer:
    Hence, the expression for the total area of the four white triangles is 12x + 36.

    Related Questions to study

    General
    Maths-

    Write the product in the standard form. (𝑥2 − 2𝑦)(𝑥2 + 2𝑦)

    (x2 − 2y)(x2 + 2y) = x2(x2 + 2y) - 2y(x2 + 2y)

    =  x2(x2) + x2(2y) - 2y(x2) - 2y(2y)

    = x4 + 2x2y - 2x2y - 4y2

    = x4 - 4y2
    Final Answer:
    Hence, the simplified form of (𝑥2 − 2𝑦)(𝑥2 + 2𝑦) is x4 - 4y2.
     

    Write the product in the standard form. (𝑥2 − 2𝑦)(𝑥2 + 2𝑦)

    Maths-General
    (x2 − 2y)(x2 + 2y) = x2(x2 + 2y) - 2y(x2 + 2y)

    =  x2(x2) + x2(2y) - 2y(x2) - 2y(2y)

    = x4 + 2x2y - 2x2y - 4y2

    = x4 - 4y2
    Final Answer:
    Hence, the simplified form of (𝑥2 − 2𝑦)(𝑥2 + 2𝑦) is x4 - 4y2.
     

    General
    Maths-

    Write the product in the standard form. (𝑥 − 2.5)(𝑥 + 2.5)

    (x − 2.5)(x + 2.5) = (x − 5 over 2)(x + 5 over 2)

    = x(x + 5 over 2) - 5 over 2(x + 5 over 2)

    =  x(x) + x(5 over 2) - 5 over 2(x) - 5 over 2(5 over 2)

    = x2 + 5 over 2x - 5 over 2x -25 over 4

    = x225 over 4

    = x2 - 6.25
    Final Answer:
    Hence, the simplified form of (𝑥 − 2.5)(𝑥 + 2.5) is x2 - 6.25.
     

    Write the product in the standard form. (𝑥 − 2.5)(𝑥 + 2.5)

    Maths-General
    (x − 2.5)(x + 2.5) = (x − 5 over 2)(x + 5 over 2)

    = x(x + 5 over 2) - 5 over 2(x + 5 over 2)

    =  x(x) + x(5 over 2) - 5 over 2(x) - 5 over 2(5 over 2)

    = x2 + 5 over 2x - 5 over 2x -25 over 4

    = x225 over 4

    = x2 - 6.25
    Final Answer:
    Hence, the simplified form of (𝑥 − 2.5)(𝑥 + 2.5) is x2 - 6.25.
     

    General
    Maths-

    Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
    5 inches, 12 inches

    Answer:
    • Hints:

      • Triangle inequality theorem
      • According to this theorem, in any triangle, sum of two sides is greater than third side,
      • a < b + c
    b < a + c
    c < a + b
      • while finding possible lengths of third side use below formula
    difference of two side < third side < sum of two sides
    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.
    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.
      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17
      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17
      • Step 2:
    difference of two side < third side < sum of two sides
      • Step 2:
    b – a < c < a + b
    12 – 5 < c < 5 + 12
    7 < c < 17
    Hence, all numbers between 7 and 17 will be the length of third side.
    • Final Answer: 
    Hence, all numbers between 7 and 17 will be the length of third side.



     

    Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
    5 inches, 12 inches

    Maths-General
    Answer:
    • Hints:

      • Triangle inequality theorem
      • According to this theorem, in any triangle, sum of two sides is greater than third side,
      • a < b + c
    b < a + c
    c < a + b
      • while finding possible lengths of third side use below formula
    difference of two side < third side < sum of two sides
    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.
    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.
      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17
      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17
      • Step 2:
    difference of two side < third side < sum of two sides
      • Step 2:
    b – a < c < a + b
    12 – 5 < c < 5 + 12
    7 < c < 17
    Hence, all numbers between 7 and 17 will be the length of third side.
    • Final Answer: 
    Hence, all numbers between 7 and 17 will be the length of third side.



     
    parallel
    General
    Maths-

    Write the product in the standard form. (3𝑎 − 4𝑏)(3𝑎 + 4𝑏)

    (3a − 4b)(3a + 4b)  = 3a(3a + 4b) - 4b(3a + 4b)
    =  3a(3a) + 3a(4b) - 4b(3a) - 4b(4b)
    = 9a2 + 12ab - 12ab - 16b2
    = 9a2 - 16b2
    Final Answer:
    Hence, the simplified form of (3𝑎 − 4𝑏)(3𝑎 + 4𝑏) is 9a2 - 16b2.
     

    Write the product in the standard form. (3𝑎 − 4𝑏)(3𝑎 + 4𝑏)

    Maths-General
    (3a − 4b)(3a + 4b)  = 3a(3a + 4b) - 4b(3a + 4b)
    =  3a(3a) + 3a(4b) - 4b(3a) - 4b(4b)
    = 9a2 + 12ab - 12ab - 16b2
    = 9a2 - 16b2
    Final Answer:
    Hence, the simplified form of (3𝑎 − 4𝑏)(3𝑎 + 4𝑏) is 9a2 - 16b2.
     
    General
    Maths-

    Write the product in the standard form. open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses

    open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses equals 1 fourth x open parentheses 1 fourth x plus 2 over 3 close parentheses minus 2 over 3 open parentheses 1 fourth x plus 2 over 3 close parentheses

    equals 1 fourth x open parentheses 1 fourth x close parentheses plus 1 fourth x open parentheses 2 over 3 close parentheses minus 2 over 3 open parentheses 1 fourth x close parentheses minus 2 over 3 open parentheses 2 over 3 close parentheses

    equals 1 over 16 x squared plus 1 over 6 x minus 1 over 6 x minus 4 over 9
    equals 1 over 16 x squared minus 4 over 9
    Final Answer:
    Hence, the simplified form of open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses text  is  end text 1 over 16 x squared minus 4 over 9.
     

    Write the product in the standard form. open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses

    Maths-General
    open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses equals 1 fourth x open parentheses 1 fourth x plus 2 over 3 close parentheses minus 2 over 3 open parentheses 1 fourth x plus 2 over 3 close parentheses

    equals 1 fourth x open parentheses 1 fourth x close parentheses plus 1 fourth x open parentheses 2 over 3 close parentheses minus 2 over 3 open parentheses 1 fourth x close parentheses minus 2 over 3 open parentheses 2 over 3 close parentheses

    equals 1 over 16 x squared plus 1 over 6 x minus 1 over 6 x minus 4 over 9
    equals 1 over 16 x squared minus 4 over 9
    Final Answer:
    Hence, the simplified form of open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses text  is  end text 1 over 16 x squared minus 4 over 9.
     

    General
    Maths-

    How is it possible that the sum of two quadratic trinomials is a linear binomial?

    Explanation:
    • We have to find out how is it possible that the sum of two quadratic trinomials is a linear binomial.
    Step 1 of 1:
    it is possible that the sum of two quadratic trinomials is a linear binomial
    If the other terms get cancel
    Example:
    2 x squared plus 5 x minus 3,
    negative 2 x squared minus 2 x plus 5
    On addition we will get 3 x plus 2, which is a linear binomial.

    How is it possible that the sum of two quadratic trinomials is a linear binomial?

    Maths-General
    Explanation:
    • We have to find out how is it possible that the sum of two quadratic trinomials is a linear binomial.
    Step 1 of 1:
    it is possible that the sum of two quadratic trinomials is a linear binomial
    If the other terms get cancel
    Example:
    2 x squared plus 5 x minus 3,
    negative 2 x squared minus 2 x plus 5
    On addition we will get 3 x plus 2, which is a linear binomial.
    parallel
    General
    Maths-

    If (3x-4) (5x+7) = 15x2-ax-28, so find the value of a?

    Answer:
    • Hint:
    ○     While evaluating the expression just put the values and perform basic operations.
    • Step by step explanation:
    ○     Given:
    ○     Two terms.
    (3x-4) (5x+7) = 15x2-ax-28
    ○     Step 1:
    ○     Simplify the right side:
    ○     (3x-4) (5x+7)
    rightwards double arrow 3x(5x+7) - 4(5x+7)
    rightwards double arrow15x2 + 21x - 20x - 28
    rightwards double arrow15x2 + x - 28
    ○     Step 1:
    ○     compare both side:
    15x2 + x - 28 =15x2- ax - 28
    By comparing we get
    a = -1
    • Final Answer:
    Hence, the value a is -1.

    If (3x-4) (5x+7) = 15x2-ax-28, so find the value of a?

    Maths-General
    Answer:
    • Hint:
    ○     While evaluating the expression just put the values and perform basic operations.
    • Step by step explanation:
    ○     Given:
    ○     Two terms.
    (3x-4) (5x+7) = 15x2-ax-28
    ○     Step 1:
    ○     Simplify the right side:
    ○     (3x-4) (5x+7)
    rightwards double arrow 3x(5x+7) - 4(5x+7)
    rightwards double arrow15x2 + 21x - 20x - 28
    rightwards double arrow15x2 + x - 28
    ○     Step 1:
    ○     compare both side:
    15x2 + x - 28 =15x2- ax - 28
    By comparing we get
    a = -1
    • Final Answer:
    Hence, the value a is -1.
    General
    Maths-

    The difference of x4+2x2-3x+7 and another polynomial is x3+x2+x-1. What is the
    another polynomial?

    Answer:
    • Hint:
    ○    Subtraction of polynomials.
    ○     Always take like terms together while performing subtraction.
    ○     In addition to polynomials only terms with the same coefficient are subtracted.
    • Step by step explanation:
    ○    Given:
    One polynomial: x4+2x2-3x+7
    Difference: x3+x2+x-1.
    ○     Step 1:
    ○     Let another polynomial be A.
    So,
    rightwards double arrow(x4+2x2-3x+7) – A = (x3+x2+x-1)
    rightwards double arrowA = (x4+2x2-3x+7) - (x3+x2+x-1)
    rightwards double arrow A = x4 + 2x2 - 3x + 7 - x3 - x2 - x + 1
    rightwards double arrow A = x4- x3 + 2x2- x2 - 3x - x + 7 + 1
    rightwards double arrow A = x4 - x3 + x2 - 4x + 8
    • Final Answer:
    Hence, another polynomial is x4 - x3 + x2 - 4x + 8.

    The difference of x4+2x2-3x+7 and another polynomial is x3+x2+x-1. What is the
    another polynomial?

    Maths-General
    Answer:
    • Hint:
    ○    Subtraction of polynomials.
    ○     Always take like terms together while performing subtraction.
    ○     In addition to polynomials only terms with the same coefficient are subtracted.
    • Step by step explanation:
    ○    Given:
    One polynomial: x4+2x2-3x+7
    Difference: x3+x2+x-1.
    ○     Step 1:
    ○     Let another polynomial be A.
    So,
    rightwards double arrow(x4+2x2-3x+7) – A = (x3+x2+x-1)
    rightwards double arrowA = (x4+2x2-3x+7) - (x3+x2+x-1)
    rightwards double arrow A = x4 + 2x2 - 3x + 7 - x3 - x2 - x + 1
    rightwards double arrow A = x4- x3 + 2x2- x2 - 3x - x + 7 + 1
    rightwards double arrow A = x4 - x3 + x2 - 4x + 8
    • Final Answer:
    Hence, another polynomial is x4 - x3 + x2 - 4x + 8.
    General
    Maths-

    Use the product of sum and difference to find 83 × 97.

    83 can be written as (90 - 7) and 97 can be written as (90 + 7)
    So, 83 × 97 can be written (90 - 7) ×  (90 + 7)
    (90 - 7) ×  (90 + 7)  = 90(90 + 7) - 7(90 + 7)

    =  90(90) + 90(7) - 7(90) - 7(7)

    = 8100 + 630 - 630 - 49

    = 8100 - 49

    = 8051
    Final Answer:
    Hence, the simplified form of 83 × 97 is 8051.
     

    Use the product of sum and difference to find 83 × 97.

    Maths-General
    83 can be written as (90 - 7) and 97 can be written as (90 + 7)
    So, 83 × 97 can be written (90 - 7) ×  (90 + 7)
    (90 - 7) ×  (90 + 7)  = 90(90 + 7) - 7(90 + 7)

    =  90(90) + 90(7) - 7(90) - 7(7)

    = 8100 + 630 - 630 - 49

    = 8100 - 49

    = 8051
    Final Answer:
    Hence, the simplified form of 83 × 97 is 8051.
     

    parallel
    General
    Maths-

    Determine the gradient and y-intercept from the following equation: 4x + y = -10

    Hint:
    Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, we compare the equation with the standard form to get the slope and the y-intercept.
    Step by step solution:
    The given equation of the line is
    4x + y = -10
    We need to convert this equation in the slope-intercept form of the line, which is
    y = mx + c, where m is the slope of the line and c is the y – intercept.
    Rewriting the given equation, that is, keeping only the term containing y in the left hand side, we get
    y = -4x - 10
    Comparing the above equation with y = mx + c, we get
    m = -4 ;c = -10
    Thus, we get
    Gradient = -4
    y-intercept = -10
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative a over b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c=0. Using this method, be careful to check that the equation is in general form before applying the formula.

    Determine the gradient and y-intercept from the following equation: 4x + y = -10

    Maths-General
    Hint:
    Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, we compare the equation with the standard form to get the slope and the y-intercept.
    Step by step solution:
    The given equation of the line is
    4x + y = -10
    We need to convert this equation in the slope-intercept form of the line, which is
    y = mx + c, where m is the slope of the line and c is the y – intercept.
    Rewriting the given equation, that is, keeping only the term containing y in the left hand side, we get
    y = -4x - 10
    Comparing the above equation with y = mx + c, we get
    m = -4 ;c = -10
    Thus, we get
    Gradient = -4
    y-intercept = -10
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative a over b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c=0. Using this method, be careful to check that the equation is in general form before applying the formula.
    General
    Maths-

    Use the product of sum and difference to find 32 × 28.

    32 can be written as (30 + 2) and 28 can be written as (30 - 2)
    So, 32 × 28 can be written (30 + 2) ×  (30 - 2)
    (30 + 2) ×  (30 - 2)  = 30(30 - 2) + 2(30 - 2)

    =  30(30) + 30(-2) + 2(30) + 2(-2)

    = 900 - 60 + 60 - 4

    = 900 - 4

    = 896
    Final Answer:
    Hence, the simplified form of 32 × 28 is 896.
     

    Use the product of sum and difference to find 32 × 28.

    Maths-General
    32 can be written as (30 + 2) and 28 can be written as (30 - 2)
    So, 32 × 28 can be written (30 + 2) ×  (30 - 2)
    (30 + 2) ×  (30 - 2)  = 30(30 - 2) + 2(30 - 2)

    =  30(30) + 30(-2) + 2(30) + 2(-2)

    = 900 - 60 + 60 - 4

    = 900 - 4

    = 896
    Final Answer:
    Hence, the simplified form of 32 × 28 is 896.
     

    General
    Maths-

    The sum of two expressions is x3-x2+3x-2. If one of them is x2 + 5x - 6, what is the
    other?

    Answer:
    • Hint:
    ○      Addition of polynomials.
    ○      Always take like terms together while performing addition.
    ○      In subtraction of polynomials only coefficients are subtracted.
    • Step by step explanation:
    ○      Given:
    Sum:  x3 -x2 + 3x- 2
    Term: x2 + 5x- 6
    ○      Step 1:
    ○      Let the other term be A.
    As given sum is x3 -x2 + 3x- 2
    rightwards double arrow A + x2 + 5x- 6 = x3 -x2 + 3x- 2
    rightwards double arrow A = x3 -x2 + 3x- 2 ) - ( x2 + 5x- 6 )
    rightwards double arrow A = x3 -x2 + 3x - 2 - x2 - 5x + 6
    rightwards double arrow A = x3 -x2 - x2 + 3x - 5x - 2 + 6
    rightwards double arrow A = x3 -2x2 - 2x + 4
    • Final Answer:
    Hence, the other term is x3 -2x2 - 2x + 4.

    The sum of two expressions is x3-x2+3x-2. If one of them is x2 + 5x - 6, what is the
    other?

    Maths-General
    Answer:
    • Hint:
    ○      Addition of polynomials.
    ○      Always take like terms together while performing addition.
    ○      In subtraction of polynomials only coefficients are subtracted.
    • Step by step explanation:
    ○      Given:
    Sum:  x3 -x2 + 3x- 2
    Term: x2 + 5x- 6
    ○      Step 1:
    ○      Let the other term be A.
    As given sum is x3 -x2 + 3x- 2
    rightwards double arrow A + x2 + 5x- 6 = x3 -x2 + 3x- 2
    rightwards double arrow A = x3 -x2 + 3x- 2 ) - ( x2 + 5x- 6 )
    rightwards double arrow A = x3 -x2 + 3x - 2 - x2 - 5x + 6
    rightwards double arrow A = x3 -x2 - x2 + 3x - 5x - 2 + 6
    rightwards double arrow A = x3 -2x2 - 2x + 4
    • Final Answer:
    Hence, the other term is x3 -2x2 - 2x + 4.
    parallel
    General
    Maths-

    Use the square of a binomial to find the value. 722

    722 can be written as  (70 + 2)2 which can be further written as (70 + 2)(70 + 2)
    (70 + 2)(70 + 2) = 70(70 + 2) + 2(70 + 2)

    =  70(70) +  70(2) + 2(70) + 2(2)

    = 4900 + 140 + 140 + 4

    = 4900 + 280 + 4

    = 5184
    Final Answer:
    Hence, the value of 722 is 5184.

    Use the square of a binomial to find the value. 722

    Maths-General
    722 can be written as  (70 + 2)2 which can be further written as (70 + 2)(70 + 2)
    (70 + 2)(70 + 2) = 70(70 + 2) + 2(70 + 2)

    =  70(70) +  70(2) + 2(70) + 2(2)

    = 4900 + 140 + 140 + 4

    = 4900 + 280 + 4

    = 5184
    Final Answer:
    Hence, the value of 722 is 5184.

    General
    Maths-

    What is the gradient of a line parallel to the line whose equation -2x + y = -7 is:

    Hint:
    The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.
    Step by step solution:
    The given equation of the line is
    -2x + y = -7
    We convert this equation in the slope intercept form, which is
    y = mx + c
    Where m is the slope of the line and c is the y-intercept.
    We rewrite the equation -2x + y - 7, as below
    y = 2x - 7
    Comparing with y = mx + c, we get that m = 2
    Thus, the gradient of line -2x + y = 7 is m = 2.
    We know that the gradient of any two parallel lines in the xy plane is always equal.
    Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative a over b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get m equals negative fraction numerator negative 2 over denominator 1 end fraction equals 2

    What is the gradient of a line parallel to the line whose equation -2x + y = -7 is:

    Maths-General
    Hint:
    The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.
    Step by step solution:
    The given equation of the line is
    -2x + y = -7
    We convert this equation in the slope intercept form, which is
    y = mx + c
    Where m is the slope of the line and c is the y-intercept.
    We rewrite the equation -2x + y - 7, as below
    y = 2x - 7
    Comparing with y = mx + c, we get that m = 2
    Thus, the gradient of line -2x + y = 7 is m = 2.
    We know that the gradient of any two parallel lines in the xy plane is always equal.
    Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative a over b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get m equals negative fraction numerator negative 2 over denominator 1 end fraction equals 2
    General
    Maths-

    Two sides of a rectangle are (3p+5q) units and ( 5p-7q ) units. What is its area?

    Answer:
    • Hint:
    The concept used in the question is the area of a rectangle.
    The area of the rectangle is the product of sides.
    • Step by step explanation:
    ○     Given:
    Two sides of a rectangle
    (3p+5q) units and ( 5p-7q ) units.
    ○     Step 1:
    We know, the area of rectangle is product of its sides
    i.e. area = side × side
    So,
    Area = (3p+5q) × (5p-7q)
    = 3p (5p -7q) + 5q(5p-7q)
    = 15p2 - 21pq + 25pq - 35q2
    = 15p2 + 4pq - 35q2 sq. units
    • Final Answer:
    Hence, the area of the rectangle is 15p2 + 4pq - 35q2 sq. units.

    Two sides of a rectangle are (3p+5q) units and ( 5p-7q ) units. What is its area?

    Maths-General
    Answer:
    • Hint:
    The concept used in the question is the area of a rectangle.
    The area of the rectangle is the product of sides.
    • Step by step explanation:
    ○     Given:
    Two sides of a rectangle
    (3p+5q) units and ( 5p-7q ) units.
    ○     Step 1:
    We know, the area of rectangle is product of its sides
    i.e. area = side × side
    So,
    Area = (3p+5q) × (5p-7q)
    = 3p (5p -7q) + 5q(5p-7q)
    = 15p2 - 21pq + 25pq - 35q2
    = 15p2 + 4pq - 35q2 sq. units
    • Final Answer:
    Hence, the area of the rectangle is 15p2 + 4pq - 35q2 sq. units.
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