What is expand (a^2-b^3)^3 ?

The solution to expand (a^2-b^3)^3 is a^6-3a^4b^3+3a^2b^6-b^9

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expand (a^2-b^3)^3

expand

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

a^{6} - 3 a^{4} b^{3} + 3 a^{2} b^{6} - b^{9}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(a^{2})^{3} - 3 (a^{2})^{2} b^{3} + 3 a^{2} (b^{3})^{2} - (b^{3})^{3} : a^{6} - 3 a^{4} b^{3} + 3 a^{2} b^{6} - b^{9}

= a^{6} - 3 a^{4} b^{3} + 3 a^{2} b^{6} - b^{9}

3 x^{2} - 5 x^{2} + 2

p^{2} - 2 p + \frac{1}{4}

6 \cdot 6^{6}

(- 4 r)^{2}

\frac{70}{x - 7} - \frac{16 x}{x - 7}

What is expand (a^2-b^3)^3 ?
The solution to expand (a^2-b^3)^3 is a^6-3a^4b^3+3a^2b^6-b^9