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)

3 \frac{3}{8}

(3 x - 5 y)^{3}

\frac{- 7 - 4 i}{2 - 7 i}

(x - 5) (x + 1) (x - 2)

\frac{50}{7}