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Popular >

expand (x+1/2)^3

Solution

expand

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

Solution

\frac{8 x ^{3} + 6 x + 12 x ^{2} + 1}{8}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

x^{3} + 3 x^{2} \frac{1}{2} + 3 x (\frac{1}{2})^{2} + (\frac{1}{2})^{3} : \frac{8 x ^{3} + 6 x + 12 x ^{2} + 1}{8}

= \frac{8 x ^{3} + 6 x + 12 x ^{2} + 1}{8}

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Frequently Asked Questions (FAQ)

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