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)

- 30 x^{3} + 54 x^{2} - 24 x^{\frac{1}{6}} x^{1}

k \cdot (\frac{- 3}{k})^{2} + 6 \cdot (\frac{- 3}{k})

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

(- 5 a^{3} b^{6})^{3}

\frac{3}{x} + 1 + \frac{5}{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)