Maths-
General
Easy

Question

Use polynomial identities to factor the polynomials or simplify the expressions :
open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses

hintHint:

open parentheses a squared minus b squared close parentheses equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis , where a and b can be real values, variables or multiples of both. We are asked to use polynomial identities to simplify the given expressions.

The correct answer is: lowest form.


    Step 1 of 2:
    The given expression is open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses . It can be written as open parentheses 1 fourth x cubed close parentheses squared minus open parentheses 5 y squared close parentheses squared. It is of the form open parentheses a squared minus b squared close parentheses where a equals 1 fourth x cubed straight & b equals 5 y squared
    Step 2 of 2:
    Use the polynomial identity to simplify the expression;

    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 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses equals open parentheses 1 fourth x cubed close parentheses squared minus open parentheses 5 y squared close parentheses squared end cell row cell equals open parentheses 1 fourth x cubed minus 5 y squared close parentheses open parentheses 1 fourth x cubed plus 5 y squared close parentheses end cell end table
    Thus, the factor form is open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses equals open parentheses 1 fourth x cubed minus 5 y squared close parentheses open parentheses 1 fourth x cubed plus 5 y squared close parentheses

    We can use multiple identities to factorize an expression. Our aim is to reduce the expression into the lowest form.

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