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Question

Use polynomial identities to multiply the expressions ? open parentheses 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared 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 find the product of the expression.

The correct answer is: (25x2 - 15y2)(25x2 + 15y2) = 625x4 - 225y4.


    Step 1 of 2:
    The given expression is open parentheses 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared close parentheses . It is of the form left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis where a equals 25 x squared straight & b equals 15 y squared.
    Step 2 of 2:
    Use the polynomial identity open parentheses a squared minus b squared close parentheses equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis to find the product of 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 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared close parentheses equals open parentheses 25 x squared close parentheses squared minus open parentheses 15 y squared close parentheses squared end cell row cell equals 625 x to the power of 4 minus 225 y to the power of 4 end cell end table
    Thus, the product is open parentheses 25 x squared minus 15 y squared close parentheses open parentheses 25 x squared plus 15 y squared close parentheses equals 625 x to the power of 4 minus 225 y to the power of 4 .

    Polynomial identities are equations that are true for all possible values of the variable. We can perform polynomial multiplication by applying the distributive property to the multiplication of polynomials.

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