What is factor u^3w^3+1/8 ?

The solution to factor u^3w^3+1/8 is (uw+1/2)(u^2w^2-(uw)/2+1/4)

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factor u^3w^3+1/8

factor

u^{3} w^{3} + \frac{1}{8}

(u w + \frac{1}{2}) (u^{2} w^{2} - \frac{u w}{2} + \frac{1}{4})

Solution steps

u^{3} w^{3} + \frac{1}{8}

Rewrite

u^{3} w^{3}

(u w)^{3}

= (u w)^{3} + \frac{1}{8}

Apply radical rule:

a = (a)^{2}

Apply Sum of Cubes Formula:

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

= (u w + \frac{1}{2}) ((u w)^{2} - \frac{u w}{2} + (\frac{1}{2})^{2})

Refine

= (u w + \frac{1}{2}) ((u w)^{2} - \frac{u w}{2} + \frac{1}{4})

Simplify

(u w + \frac{1}{2}) ((u w)^{2} - \frac{u w}{2} + \frac{1}{4}) : (u w + \frac{1}{2}) (u^{2} w^{2} - \frac{u w}{2} + \frac{1}{4})

= (u w + \frac{1}{2}) (u^{2} w^{2} - \frac{u w}{2} + \frac{1}{4})

\frac{x ^{3} - 1}{x ^{4} - 1}

+ 2 x y - 6 y + x z - 3 z

(5) - (3)

tan^{5} (x) + cot^{5} (x)

cosh (n x) + sin (h) (n x)

What is factor u^3w^3+1/8 ?
The solution to factor u^3w^3+1/8 is (uw+1/2)(u^2w^2-(uw)/2+1/4)