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

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

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expand (x-5x^2)^3

expand

(x - 5 x^{2})^{3}

x^{3} - 15 x^{4} + 75 x^{5} - 125 x^{6}

Solution steps

(x - 5 x^{2})^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

= x^{3} - 15 x^{4} + 75 x^{5} - 125 x^{6}

(\frac{( 3 x ^{5} )}{( y ^{6} )})^{0}

144 - 4 x^{2}

(42 - x)^{2}

x + 1 x + 2 x + 3 x + 4 - 15

x^{3} + 3 x + 4

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