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Popular >

expand (2n+1)^3

Solution

expand

(2 n + 1)^{3}

Solution

8 n^{3} + 12 n^{2} + 6 n + 1

Solution steps

(2 n + 1)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

(2 n)^{3} + 3 (2 n)^{2} \cdot 1 + 3 \cdot 2 n \cdot 1^{2} + 1^{3} : 8 n^{3} + 12 n^{2} + 6 n + 1

= 8 n^{3} + 12 n^{2} + 6 n + 1

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Frequently Asked Questions (FAQ)

What is expand (2n+1)^3 ?
The solution to expand (2n+1)^3 is 8n^3+12n^2+6n+1