What is expand (1+x/2)^3 ?

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

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expand (1+x/2)^3

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

(3 - 3 i)^{5}

(3 - t)^{2}

\frac{x ^{2} - 8 x + 12}{( x - 4 ) ^{2}}

x^{\frac{1}{3}} (x^{2} - 42)

\frac{\frac{d}{d x} ( ( y ) ( y ^{2} + 2 x y ) )}{x ^{2}}

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