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

The solution to expand (a^2+2b)^3 is a^6+6a^4b+12a^2b^2+8b^3

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expand (a^2+2b)^3

expand

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

a^{6} + 6 a^{4} b + 12 a^{2} b^{2} + 8 b^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(a^{2})^{3} + 3 (a^{2})^{2} \cdot 2 b + 3 a^{2} (2 b)^{2} + (2 b)^{3} : a^{6} + 6 a^{4} b + 12 a^{2} b^{2} + 8 b^{3}

= a^{6} + 6 a^{4} b + 12 a^{2} b^{2} + 8 b^{3}

\frac{2}{5} - \frac{2}{5}

(1 - x^{2})^{5}

(3 x^{2} - 6 x + 11) - (10 x^{2} - 4 x + 6)

\frac{24 z + 13}{z ^{2} - 100} - \frac{23 z + 3}{z ^{2} - 100}

\frac{9}{2} + 6

What is expand (a^2+2b)^3 ?
The solution to expand (a^2+2b)^3 is a^6+6a^4b+12a^2b^2+8b^3