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

The solution to expand (2x-y^2)^3 is 8x^3-12x^2y^2+6xy^4-y^6

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expand (2x-y^2)^3

expand

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

8 x^{3} - 12 x^{2} y^{2} + 6 x y^{4} - y^{6}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(2 x)^{3} - 3 (2 x)^{2} y^{2} + 3 \cdot 2 x (y^{2})^{2} - (y^{2})^{3} : 8 x^{3} - 12 x^{2} y^{2} + 6 x y^{4} - y^{6}

= 8 x^{3} - 12 x^{2} y^{2} + 6 x y^{4} - y^{6}

(x - 3) (x + 2) (x + 3) (x + 8) + 56

\frac{5}{sin ^{2} ( a )} - 5 cot^{2} (a)

\frac{a}{2} + \frac{a ^{3}}{2} + \frac{a ^{5}}{2}

a^{3} b^{2} + a^{2} b^{3}

y^{5} - y^{3} - y^{2} + 1

What is expand (2x-y^2)^3 ?
The solution to expand (2x-y^2)^3 is 8x^3-12x^2y^2+6xy^4-y^6