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Popular >

expand (1+a^2)^3

Solution

expand

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

Solution

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

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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