Maths-
General
Easy

Question

How can you use polynomial identities to factor polynomials and simplify numerical expressions ? m to the power of 8 minus 9 n to the power of 10

Hint:

a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis, where a and b can be real numbers, variables or multiples of both. We are asked to explain on how the polynomial identities can be used to factorize polynomials and simplify them.

The correct answer is: m8 - 9n10 = (m4 - 3n5)(m4 + 3n5)


    Step 1 of 2:
    The given expression is m to the power of 8 minus 9 n to the power of 10. It can be written as, open parentheses m to the power of 4 close parentheses squared minus open parentheses 3 n to the power of 5 close parentheses squared. Here, a equals m to the power of 4 straight & b equals 3 n to the power of 5 . Thus, we can apply the identity a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis to simplify the expression.
    Step 2 of 2:
    Simplifying the expression, we get:

    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 m to the power of 8 minus 9 n to the power of 10 equals open parentheses m to the power of 4 close parentheses squared minus open parentheses 3 n to the power of 5 close parentheses squared end cell row cell equals open parentheses m to the power of 4 minus 3 n to the power of 5 close parentheses open parentheses m to the power of 4 plus 3 n to the power of 5 close parentheses end cell end table
    Thus, the simplified expression is: m to the power of 8 minus 9 n to the power of 10 equals open parentheses m to the power of 4 minus 3 n to the power of 5 close parentheses open parentheses m to the power of 4 plus 3 n to the power of 5 close parentheses
     

    We use polynomial identities to reduce the time and space while solving polynomial expressions and equations.

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