Maths-
General
Easy

Question

Use polynomial identities to multiply the expressions ?
open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses

The correct answer is: Thus, the product is (25x^2-15y^2)(25x^2+15y^2)=625x^4-225y^4.


    ANSWER:
    Hint:
    open parentheses straight a squared minus straight b squared close parentheses equals left parenthesis straight a minus straight b right parenthesis left parenthesis straight a plus straight 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.
    Step 1 of 2:
    The given expression is open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses.text  It is of the form  end text left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis text  where  end text a equals 25 x squared straight & b equals 15 y squared text .  end text
    Step 2 of 2:
    Use the polynomial identity open parentheses straight a squared minus straight b squared close parentheses equals left parenthesis straight a minus straight b right parenthesis left parenthesis straight a plus straight 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 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table
    Note:
    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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