What is expand (3u+2v)^3 ?

The solution to expand (3u+2v)^3 is 27u^3+54u^2v+36uv^2+8v^3

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expand (3u+2v)^3

expand

(3 u + 2 v)^{3}

27 u^{3} + 54 u^{2} v + 36 u v^{2} + 8 v^{3}

Solution steps

(3 u + 2 v)^{3}

Apply Perfect Cube Formula:

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

(3 u + 2 v)^{3} = (3 u)^{3} + 3 (3 u)^{2} \cdot 2 v + 3 \cdot 3 u (2 v)^{2} + (2 v)^{3}

= (3 u)^{3} + 3 (3 u)^{2} \cdot 2 v + 3 \cdot 3 u (2 v)^{2} + (2 v)^{3}

Simplify

(3 u)^{3} + 3 (3 u)^{2} \cdot 2 v + 3 \cdot 3 u (2 v)^{2} + (2 v)^{3} : 27 u^{3} + 54 u^{2} v + 36 u v^{2} + 8 v^{3}

= 27 u^{3} + 54 u^{2} v + 36 u v^{2} + 8 v^{3}

(- 3 i) (10 i)

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\frac{3 x + 2}{x + 4} - \frac{x - 6}{x + 4}

What is expand (3u+2v)^3 ?
The solution to expand (3u+2v)^3 is 27u^3+54u^2v+36uv^2+8v^3