What is expand (x+2y)^3+512 ?

The solution to expand (x+2y)^3+512 is x^3+6x^2y+12xy^2+8y^3+512

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expand (x+2y)^3+512

expand

(x + 2 y)^{3} + 512

x^{3} + 6 x^{2} y + 12 x y^{2} + 8 y^{3} + 512

Solution steps

(x + 2 y)^{3} + 512

Apply Perfect Cube Formula:

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

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

= x^{3} + 3 x^{2} \cdot 2 y + 3 x (2 y)^{2} + (2 y)^{3} + 512

Simplify

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

= x^{3} + 6 x^{2} y + 12 x y^{2} + 8 y^{3} + 512

5.8 x \cdot 105 \cdot 4 \cdot 3 \cdot 1064

z^{4} + (- 24) z^{2} + 400

\frac{\frac{x}{x}}{6} + \frac{x}{24}

(- i)^{4} n

- 2 a \cdot b^{2} - s

What is expand (x+2y)^3+512 ?
The solution to expand (x+2y)^3+512 is x^3+6x^2y+12xy^2+8y^3+512