Maths-
General
Easy

Question

Use polynomial identities to factor each polynomial :
open parentheses 8 x to the power of 6 minus y cubed close parentheses

The correct answer is: Hence, the factor is: .


    ANSWER:
    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 use polynomial identities to factor the given polynomial.
    Step 1 of 2:
    The given expression is open parentheses 8 x to the power of 6 minus y cubed close parentheses . It can be written as open parentheses 2 x squared close parentheses cubed minus y cubed . This is of the form a cubed minus b cubed where .
    a equals 2 x squared straight & b equals y
    Step 2 of 2:
    Substitute the values in the expansion to get the factor form. Thus, we have:
    open parentheses 8 x to the power of 6 minus y cubed close parentheses equals open parentheses 2 x squared close parentheses cubed minus y cubed
    equals open parentheses 2 x squared minus y close parentheses open parentheses open parentheses 2 x squared close parentheses squared plus open parentheses 2 x squared close parentheses left parenthesis y right parenthesis plus left parenthesis y right parenthesis squared close
    equals open parentheses 2 x squared minus y close parentheses open parentheses 4 x to the power of 4 plus 2 y x squared plus y squared close parentheses
    Hence, the factor is: open parentheses 8 x to the power of 6 minus y cubed close parentheses equals open parentheses 2 x squared minus y close parentheses open parentheses 4 x to the power of 4 plus 2 y x squared plus y squared close parentheses .
    Note:
    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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