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

The solution to expand (5x^3*y^2-x)^3 is 125x^9y^6-75x^7y^4+15x^5y^2-x^3

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expand (5x^3*y^2-x)^3

expand

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

125 x^{9} y^{6} - 75 x^{7} y^{4} + 15 x^{5} y^{2} - x^{3}

Solution steps

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

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

Simplify

(5 x^{3} y^{2})^{3} - 3 (5 x^{3} y^{2})^{2} x + 3 \cdot 5 x^{3} y^{2} x^{2} - x^{3} : 125 x^{9} y^{6} - 75 x^{7} y^{4} + 15 x^{5} y^{2} - x^{3}

= 125 x^{9} y^{6} - 75 x^{7} y^{4} + 15 x^{5} y^{2} - x^{3}

(\frac{x + 1}{2 y})^{3}

\frac{( 2 x + 3 y )}{( 3 x + 7 y )}

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

49 \cdot (2 x + 3 y)^{2} - 70 (4 x^{2} - 9 y^{2}) + 25 \cdot (2 x - 3 y)^{2}

(x - 1) (x + 3) - (\frac{( 2 x - 2 )}{( x + 2 )})

What is expand (5x^3*y^2-x)^3 ?
The solution to expand (5x^3*y^2-x)^3 is 125x^9y^6-75x^7y^4+15x^5y^2-x^3