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

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

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

expand

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

125 x^{6} y^{3} + 150 x^{5} y^{2} + 60 x^{4} y + 8 x^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

= 125 x^{6} y^{3} + 150 x^{5} y^{2} + 60 x^{4} y + 8 x^{3}

7 y^{2} - \frac{11}{3} y - \frac{2}{3}

9 x^{2} - 12 x + 3

68 x^{25} + 68 x^{5}

(8 c - d) (c + 9 d) - 5 (d - 8 c)

(\frac{( 2 z ^{4} )}{( 3 z ^{7} )})^{- 3}

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