What is (x^4-4096)/(x-8) ?

The solution to (x^4-4096)/(x-8) is (x^2+64)(x+8)

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simplify (x^4-4096)/(x-8)

simplify

\frac{x ^{4} - 4096}{x - 8}

(x^{2} + 64) (x + 8)

Solution steps

\frac{x ^{4} - 4096}{x - 8}

Apply exponent rules

= \frac{( x ^{2} ) ^{2} - 6 4 ^{2}}{x - 8}

Apply Difference of Two Squares Formula:

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

(x^{2})^{2} - 6 4^{2} = (x^{2} + 64) (x^{2} - 64)

= \frac{( x ^{2} + 64 ) ( x ^{2} - 64 )}{x - 8}

Factor

x^{2} - 64 : (x + 8) (x - 8)

= \frac{( x ^{2} + 64 ) ( x + 8 ) ( x - 8 )}{x - 8}

Cancel the common factor:

x - 8

= (x^{2} + 64) (x + 8)

x^{2} + 1 \times x^{2} + 1

y^{2} y

s (s + 7) (s + 11)

7 x \times 7 x

7 x \times x