Question
What must be subtracted from 3x2-5xy -2y2-3 to get 5x2-7xy -3y2+3x
Hint:
Subtraction of polynomials.
○ Always take like terms together while performing subtraction.
○ In addition to polynomials only terms with the same coefficient are subtracted.
The correct answer is: Hence, the other term must subtract is - 2x2 + y2 + 2xy - 3x - 3.
Answer:
Step by step explanation:
○ Given:
Terms:
3x2-5xy -2y2-3
5x2-7xy -3y2+3x
○ Step 1:
○ Let A must be subtracted from 3x2-5xy -2y2-3 to get 5x2-7xy -3y2+3x.
So,
3x2-5xy -2y2-3 - A = 5x2-7xy -3y2+3x
A = (3x2-5xy -2y2-3) - ( 5x2-7xy -3y2+3x )
A = 3x2-5xy -2y2- 3- 5x2 + 7xy + 3y2 - 3x
A = 3x2 - 5x2 + 3y2 -2y2 -5xy + 7xy - 3x - 3
A = - 2x2 + y2 + 2xy - 3x - 3
A = - 2x2 + y2 + 2xy - 3x - 3.
- Final Answer:
Hence, the other term must subtract is - 2x2 + y2 + 2xy - 3x - 3.
○ Step 1:
○ Let A must be subtracted from 3x2-5xy -2y2-3 to get 5x2-7xy -3y2+3x.
So,
Related Questions to study
𝐴𝑃 is the perpendicular bisector of 𝐵𝐶.
a. What segment lengths in the diagram are equal?
b. Is A on 𝐴𝑃?
![](data:image/png;base64,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)
𝐴𝑃 is the perpendicular bisector of 𝐵𝐶.
a. What segment lengths in the diagram are equal?
b. Is A on 𝐴𝑃?
![](data:image/png;base64,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)
Use the square of a binomial to find the value. 562
Use the square of a binomial to find the value. 562
Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive odd numbers is 1 less than a perfect square.
Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive odd numbers is 1 less than a perfect square.
Name the polynomial based on its degree and number of terms.
![5 x y squared minus 3](data:image/png;base64,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)
Name the polynomial based on its degree and number of terms.
![5 x y squared minus 3](data:image/png;base64,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)
In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
ii)How many answers did each school get correct in the final round?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.
¶The standard form of a linear equation in one variable is: ax + b = 0
Where,
The letters 'a' and 'b' are real numbers.
'a' and 'b' are both greater than zero.
In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
ii)How many answers did each school get correct in the final round?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.
¶The standard form of a linear equation in one variable is: ax + b = 0
Where,
The letters 'a' and 'b' are real numbers.
'a' and 'b' are both greater than zero.