What is expand (x^2+2y)^3 ?

The solution to expand (x^2+2y)^3 is x^6+6x^4y+12x^2y^2+8y^3

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expand (x^2+2y)^3

expand

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

x^{6} + 6 x^{4} y + 12 x^{2} y^{2} + 8 y^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

(x^{2} + 2 y)^{3} = (x^{2})^{3} + 3 (x^{2})^{2} \cdot 2 y + 3 x^{2} (2 y)^{2} + (2 y)^{3}

= (x^{2})^{3} + 3 (x^{2})^{2} \cdot 2 y + 3 x^{2} (2 y)^{2} + (2 y)^{3}

Simplify

(x^{2})^{3} + 3 (x^{2})^{2} \cdot 2 y + 3 x^{2} (2 y)^{2} + (2 y)^{3} : x^{6} + 6 x^{4} y + 12 x^{2} y^{2} + 8 y^{3}

= x^{6} + 6 x^{4} y + 12 x^{2} y^{2} + 8 y^{3}

- 8128 + 50

(4 x)^{- 2} x^{4}

1 4^{4}

\frac{32 5}{4 5}

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

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