What is expand (u+ve^w)^3 ?

The solution to expand (u+ve^w)^3 is u^3+3e^wu^2v+3e^{2w}uv^2+e^{3w}v^3

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expand (u+ve^w)^3

expand

(u + v e^{w})^{3}

u^{3} + 3 e^{w} u^{2} v + 3 e^{2 w} u v^{2} + e^{3 w} v^{3}

Solution steps

(u + v e^{w})^{3}

= (u + e^{w} v)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = u, b = v e^{w}

= u^{3} + 3 u^{2} v e^{w} + 3 u (v e^{w})^{2} + (v e^{w})^{3}

Simplify

u^{3} + 3 u^{2} v e^{w} + 3 u (v e^{w})^{2} + (v e^{w})^{3} : u^{3} + 3 e^{w} u^{2} v + 3 e^{2 w} u v^{2} + e^{3 w} v^{3}

= u^{3} + 3 e^{w} u^{2} v + 3 e^{2 w} u v^{2} + e^{3 w} v^{3}

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

(2 + 3 y + y^{2})^{6}

\frac{( 2 x + 5 ) ( x - 4 )}{2}

4 \times 548

\frac{1 - 5 x}{5 ( 1 - x ) ( 1 + x )}

What is expand (u+ve^w)^3 ?
The solution to expand (u+ve^w)^3 is u^3+3e^wu^2v+3e^{2w}uv^2+e^{3w}v^3