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Popular >

expand ((x^2)+1)^3

Solution

expand

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

Solution

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

Solution steps

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

Simplify

(x^{2}) + 1 : x^{2} + 1

= (x^{2} + 1)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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