What is expand (3a^2b+2b^2)^3 ?

The solution to expand (3a^2b+2b^2)^3 is 27a^6b^3+54a^4b^4+36a^2b^5+8b^6

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expand (3a^2b+2b^2)^3

expand

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

27 a^{6} b^{3} + 54 a^{4} b^{4} + 36 a^{2} b^{5} + 8 b^{6}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 a^{2} b)^{3} + 3 (3 a^{2} b)^{2} \cdot 2 b^{2} + 3 \cdot 3 a^{2} b (2 b^{2})^{2} + (2 b^{2})^{3} : 27 a^{6} b^{3} + 54 a^{4} b^{4} + 36 a^{2} b^{5} + 8 b^{6}

= 27 a^{6} b^{3} + 54 a^{4} b^{4} + 36 a^{2} b^{5} + 8 b^{6}

(3 - 2 i) + (4 + 5 i)

- 6 \cdot 1

\frac{7}{63}

(6 - \frac{1}{2} a)^{6}

\frac{cos ( x )}{1 - sin ( x )} + \frac{cos ( x )}{1 + sin ( x )}

What is expand (3a^2b+2b^2)^3 ?
The solution to expand (3a^2b+2b^2)^3 is 27a^6b^3+54a^4b^4+36a^2b^5+8b^6