What is expand (x+4y)^3 ?

The solution to expand (x+4y)^3 is x^3+12x^2y+48xy^2+64y^3

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expand (x+4y)^3

expand

(x + 4 y)^{3}

x^{3} + 12 x^{2} y + 48 x y^{2} + 64 y^{3}

Solution steps

(x + 4 y)^{3}

Apply Perfect Cube Formula:

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

(x + 4 y)^{3} = x^{3} + 3 x^{2} \cdot 4 y + 3 x (4 y)^{2} + (4 y)^{3}

= x^{3} + 3 x^{2} \cdot 4 y + 3 x (4 y)^{2} + (4 y)^{3}

Simplify

x^{3} + 3 x^{2} \cdot 4 y + 3 x (4 y)^{2} + (4 y)^{3} : x^{3} + 12 x^{2} y + 48 x y^{2} + 64 y^{3}

= x^{3} + 12 x^{2} y + 48 x y^{2} + 64 y^{3}

2 x^{3} \cdot 7 x^{4} x (3 x)^{2}

(2 x - 3 y)^{2} - (3 y + 4 y)^{2}

22 \cdot x^{2} + 9 x + 52

2 y^{2} - \frac{y}{3} + 3 \frac{y ^{2}}{2} - y

a^{2} b^{2} + 2 b (a^{2} + 1) + a^{2} - b^{2} - 1

What is expand (x+4y)^3 ?
The solution to expand (x+4y)^3 is x^3+12x^2y+48xy^2+64y^3