Maths-
General
Easy

Question

Explain how to use a polynomial identity to factor 8 x to the power of 6 minus 27 y cubed .

Hint:

a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses, where a and b can be real values, variables or multiples of both.
We are asked to explain how to use a polynomial identity to factor 8 x to the power of 6 minus 27 y cubed

The correct answer is: polynomial



    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.
    The given polynomial is 8 x to the power of 6 minus 27 y squared . It can be written as: open parentheses 2 x squared close parentheses cubed minus left parenthesis 3 y right parenthesis cubed here a equals 2 x squared straight & b equals 3 y .
    Step 2 of 2:
    Substitute the values of 8 x to the power of 6 minus 27 y cubed in the identity;

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell open parentheses 2 x squared close parentheses cubed minus left parenthesis 3 y right parenthesis cubed equals open parentheses 2 x squared minus 3 y close parentheses open parentheses open parentheses 2 x squared close parentheses squared plus open parentheses 2 x squared close parentheses left parenthesis 3 y right parenthesis plus left parenthesis 3 y right parenthesis squared close end cell row cell equals open parentheses 2 x squared minus 3 y close parentheses open parentheses 4 x to the power of 4 plus 6 x squared y plus 9 y squared close parentheses end cell end table
    Thus, the factor is: 8 x to the power of 6 minus 27 y cubed equals open parentheses 2 x squared minus 3 y close parentheses open parentheses 4 x to the power of 4 plus 6 x squared y plus 9 y squared close parentheses

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

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