What is (x^6-64)/(x-2) ?

The solution to (x^6-64)/(x-2) is (x+2)(x^2+4+2x)(x^2+4-2x)

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simplify (x^6-64)/(x-2)

simplify

\frac{x ^{6} - 64}{x - 2}

(x + 2) (x^{2} + 4 + 2 x) (x^{2} + 4 - 2 x)

Solution steps

\frac{x ^{6} - 64}{x - 2}

Apply exponent rules

= \frac{( x ^{2} ) ^{3} - 4 ^{3}}{x - 2}

Apply Difference of Cubes Formula:

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

(x^{2})^{3} - 4^{3} = (x^{2} - 4) (x^{4} + 4 x^{2} + 4^{2})

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

Factor

x^{2} - 4 : (x + 2) (x - 2)

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

Factor

x^{4} + 4 x^{2} + 4^{2} : (x^{2} + 4 + 2 x) (x^{2} + 4 - 2 x)

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

Cancel the common factor:

x - 2

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

2 x \cdot (- x)

12 x^{2} - 204 x + 630

(\frac{x ^{7} \cdot y ^{3} \cdot x ^{4}}{x ^{6} \cdot y ^{2}})^{2}

1 + 1000 y^{3}

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

What is (x^6-64)/(x-2) ?
The solution to (x^6-64)/(x-2) is (x+2)(x^2+4+2x)(x^2+4-2x)