What is expand (3b+6a)^3 ?

The solution to expand (3b+6a)^3 is 27b^3+162b^2a+324ba^2+216a^3

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expand (3b+6a)^3

expand

(3 b + 6 a)^{3}

27 b^{3} + 162 b^{2} a + 324 b a^{2} + 216 a^{3}

Solution steps

(3 b + 6 a)^{3}

Apply Perfect Cube Formula:

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

(3 b + 6 a)^{3} = (3 b)^{3} + 3 (3 b)^{2} \cdot 6 a + 3 \cdot 3 b (6 a)^{2} + (6 a)^{3}

= (3 b)^{3} + 3 (3 b)^{2} \cdot 6 a + 3 \cdot 3 b (6 a)^{2} + (6 a)^{3}

Simplify

(3 b)^{3} + 3 (3 b)^{2} \cdot 6 a + 3 \cdot 3 b (6 a)^{2} + (6 a)^{3} : 27 b^{3} + 162 b^{2} a + 324 b a^{2} + 216 a^{3}

= 27 b^{3} + 162 b^{2} a + 324 b a^{2} + 216 a^{3}

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What is expand (3b+6a)^3 ?
The solution to expand (3b+6a)^3 is 27b^3+162b^2a+324ba^2+216a^3