What is ((x^4-81))/((x+3)) ?

The solution to ((x^4-81))/((x+3)) is (x^2+9)(x-3)

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simplify ((x^4-81))/((x+3))

simplify

\frac{( x ^{4} - 81 )}{( x + 3 )}

(x^{2} + 9) (x - 3)

Solution steps

\frac{x ^{4} - 81}{x + 3}

Apply exponent rules

= \frac{( x ^{2} ) ^{2} - 9 ^{2}}{x + 3}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(x^{2})^{2} - 9^{2} = (x^{2} + 9) (x^{2} - 9)

= \frac{( x ^{2} + 9 ) ( x ^{2} - 9 )}{x + 3}

Factor

x^{2} - 9 : (x + 3) (x - 3)

= \frac{( x ^{2} + 9 ) ( x + 3 ) ( x - 3 )}{x + 3}

Cancel the common factor:

x + 3

= (x^{2} + 9) (x - 3)

\frac{2}{21} \div \frac{2}{6}

(- 8 - 3) (- 9 + 3)

\frac{3 x ^{2} - 12 x ^{3}}{3 x ^{4}}

[(3 x)^{2}]^{- 2}

(x - 5)^{2} - 2 (x - 5)