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

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

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expand (1+y/2)^3

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

\frac{5 ( - 25 n + 25 )}{2 n}

(x - 1) (x^{2} + 4)

(4 + e^{- t} (- 4 cos (t) - 4 sin (t))) \cdot e^{t}

(sin (\frac{π x}{L}) sin (\frac{2 π y}{L}) - sin (\frac{2 π x}{L}) sin (\frac{π y}{L}))^{2}

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