Maths-
General
Easy

Question

How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
12 cubed plus 2 cubed

The correct answer is: = 1736


    ANSWER:
    Hint:
    open parentheses a cubed plus b cubed close parentheses equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheseswhere a and b can be real values, variables or multiples of both.
    We are asked to explain on how the polynomial identities can be used to factorize polynomials and simplify them.
    Step 1 of 2:
    Factoring a polynomial is the process of decomposing a polynomial into a product of two or more polynomials. This can be done with the help of identities, which would speed up the process and make it simple.
    Here, the given expression is 12 cubed plus 2 cubed where a=12 and b=2
    Step 2 of 2:
    Now, substitute the values in the identity, open parentheses a cubed plus b cubed close parentheses equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses to factorize:
    12 cubed plus 2 cubed equals left parenthesis 12 plus 2 right parenthesis open parentheses 12 squared minus 12 left parenthesis 2 right parenthesis plus 2 squared close parentheses
    equals 14 left parenthesis 144 minus 24 plus 4 right parenthesis
    negative 14 left parenthesis 124 right parenthesis
    equals 1736
    Note:
    This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.

    Related Questions to study

    General
    Maths-

    Use Pascal triangle to expand left parenthesis x plus y right parenthesis to the power of 5

    The answer cam also be found by expanding the formula of 5Cr .

    Use Pascal triangle to expand left parenthesis x plus y right parenthesis to the power of 5

    Maths-General

    The answer cam also be found by expanding the formula of 5Cr .

    General
    Maths-

    Use polynomial identities to multiply the expressions ?
    open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses

    Use polynomial identities to multiply the expressions ?
    open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses

    Maths-General
    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    27 x to the power of 9 minus 343 y to the power of 6

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    27 x to the power of 9 minus 343 y to the power of 6

    Maths-General
    parallel
    General
    Maths-

    Use polynomial identities to multiply the expressions ?

    left parenthesis 10 plus 21 right parenthesis squared

    Use polynomial identities to multiply the expressions ?

    left parenthesis 10 plus 21 right parenthesis squared

    Maths-General
    General
    Maths-

    How is ( x + y )n obtained from (x + y)n-1

    You could also get the value of left parenthesis x plus y right parenthesis to the power of n from left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent by just multiplying a (  x + y)  with left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent .

    How is ( x + y )n obtained from (x + y)n-1

    Maths-General

    You could also get the value of left parenthesis x plus y right parenthesis to the power of n from left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent by just multiplying a (  x + y)  with left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent .

    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    m to the power of 8 minus 9 n to the power of 10

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    m to the power of 8 minus 9 n to the power of 10

    Maths-General
    parallel
    General
    Maths-

    Use polynomial identities to multiply the expressions ?
    left parenthesis 7 plus 9 right parenthesis squared

    Use polynomial identities to multiply the expressions ?
    left parenthesis 7 plus 9 right parenthesis squared

    Maths-General
    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23

    This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23

    Maths-General

    This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.

    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    open parentheses 11 cubed close parentheses plus 5 cubed

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    open parentheses 11 cubed close parentheses plus 5 cubed

    Maths-General
    parallel
    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 27 x to the power of 9 minus 343 y to the power of 6

    We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 27 x to the power of 9 minus 343 y to the power of 6

    Maths-General

    We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.

    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    x cubed minus 216

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    x cubed minus 216

    Maths-General
    General
    Maths-

    Use polynomial identities to multiply the expressions ?
    103 × 97

    Use polynomial identities to multiply the expressions ?
    103 × 97

    Maths-General
    parallel
    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    open parentheses 9 m to the power of 4 close parentheses minus open parentheses 25 n to the power of 6 close parentheses

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    open parentheses 9 m to the power of 4 close parentheses minus open parentheses 25 n to the power of 6 close parentheses

    Maths-General
    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ? m to the power of 8 minus 9 n to the power of 10

    We use polynomial identities to reduce the time and space while solving polynomial expressions and equations.

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ? m to the power of 8 minus 9 n to the power of 10

    Maths-General

    We use polynomial identities to reduce the time and space while solving polynomial expressions and equations.

    General
    Maths-

    Use polynomial identities to multiply the expressions ?
    18 × 22

    Use polynomial identities to multiply the expressions ?
    18 × 22

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.