What is expand (5x^3+2y^2)^3 ?

The solution to expand (5x^3+2y^2)^3 is 125x^9+150x^6y^2+60x^3y^4+8y^6

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expand (5x^3+2y^2)^3

expand

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

125 x^{9} + 150 x^{6} y^{2} + 60 x^{3} y^{4} + 8 y^{6}

Solution steps

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

Apply Perfect Cube Formula:

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

(5 x^{3} + 2 y^{2})^{3} = (5 x^{3})^{3} + 3 (5 x^{3})^{2} \cdot 2 y^{2} + 3 \cdot 5 x^{3} (2 y^{2})^{2} + (2 y^{2})^{3}

= (5 x^{3})^{3} + 3 (5 x^{3})^{2} \cdot 2 y^{2} + 3 \cdot 5 x^{3} (2 y^{2})^{2} + (2 y^{2})^{3}

Simplify

(5 x^{3})^{3} + 3 (5 x^{3})^{2} \cdot 2 y^{2} + 3 \cdot 5 x^{3} (2 y^{2})^{2} + (2 y^{2})^{3} : 125 x^{9} + 150 x^{6} y^{2} + 60 x^{3} y^{4} + 8 y^{6}

= 125 x^{9} + 150 x^{6} y^{2} + 60 x^{3} y^{4} + 8 y^{6}

x^{6} y^{4} \cdot x y

3 x^{4} - 24 x

+ 75 a^{2} c - 45 a^{2} d - 30 b c + 18 b d

(a - b)^{2} - c^{2}

\frac{1}{2 x} + \frac{8}{9 y}

What is expand (5x^3+2y^2)^3 ?
The solution to expand (5x^3+2y^2)^3 is 125x^9+150x^6y^2+60x^3y^4+8y^6