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Popular >

expand (a^2-1)^3

Solution

expand

(a^{2} - 1)^{3}

Solution

a^{6} - 3 a^{4} + 3 a^{2} - 1

Solution steps

(a^{2} - 1)^{3}

Apply Perfect Cube Formula:

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

(a^{2} - 1)^{3} = (a^{2})^{3} - 3 (a^{2})^{2} \cdot 1 + 3 a^{2} \cdot 1^{2} - 1^{3}

= (a^{2})^{3} - 3 (a^{2})^{2} \cdot 1 + 3 a^{2} \cdot 1^{2} - 1^{3}

Simplify

(a^{2})^{3} - 3 (a^{2})^{2} \cdot 1 + 3 a^{2} \cdot 1^{2} - 1^{3} : a^{6} - 3 a^{4} + 3 a^{2} - 1

= a^{6} - 3 a^{4} + 3 a^{2} - 1

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Frequently Asked Questions (FAQ)

What is expand (a^2-1)^3 ?
The solution to expand (a^2-1)^3 is a^6-3a^4+3a^2-1