Maths-
General
Easy

Question

simplify fraction numerator 81 x to the power of 4 minus 16 x squared plus 32 x minus 16 over denominator 9 x squared minus 4 x plus 4 end fraction

hintHint:

The expansions of the identities are:
open parentheses x squared minus a squared close parentheses equals left parenthesis x plus a right parenthesis left parenthesis x minus a right parenthesis
left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis equals x squared plus left parenthesis a plus b right parenthesis x plus a b
We are asked to simplify the given expression.

The correct answer is: Hence, the simplified form is: equals 9 x 2+ 4 x - 4.


    Step 1 of 1:
    Simplify the expression and cancel out the common factors;
    fraction numerator 81 x to the power of 4 minus 16 x squared plus 32 x minus 16 over denominator 9 x squared minus 4 x plus 4 end fraction equals fraction numerator 81 x to the power of 4 minus 16 x squared plus 32 x minus 16 over denominator 9 x squared minus 4 x plus 4 end fraction
    equals fraction numerator 81 x to the power of 4 minus 16 open parentheses x squared minus 2 x plus 1 close parentheses over denominator 9 x squared minus 4 x plus 4 end fraction
    equals fraction numerator 81 x to the power of 4 minus 16 left parenthesis x minus 1 right parenthesis squared over denominator 9 x squared minus 4 x plus 4 end fraction
    equals fraction numerator open parentheses 9 x squared close parentheses squared minus left parenthesis 4 left parenthesis x minus 1 right parenthesis right parenthesis squared over denominator 9 x squared minus 4 x plus 4 end fraction
    equals fraction numerator open parentheses 9 x squared minus 4 left parenthesis x minus 1 right parenthesis open parentheses 9 x squared plus 4 left parenthesis x minus 1 right parenthesis close close over denominator 9 x squared minus 4 x plus 4 end fraction
    equals fraction numerator open parentheses 9 x squared minus 4 x plus 4 close parentheses open parentheses 9 x squared plus 4 x minus 4 close parentheses over denominator 9 x squared minus 4 x plus 4 end fraction
    equals 9 x squared plus 4 x minus 4
    Hence, the simplified form is: equals 9 x squared plus 4 x minus 4.

    Simplify means to make it simple. In mathematics, simplify is the reduction of an expression/fraction into irreducible forms.

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