What is expand ((1+2sqrt(x))^4)/2 ?

The solution to expand ((1+2sqrt(x))^4)/2 is 1/2+4sqrt(x)+12x+16x^{3/2}+8x^2

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expand ((1+2sqrt(x))^4)/2

expand

\frac{( 1 + 2 x ) ^{4}}{2}

\frac{1}{2} + 4 x + 12 x + 16 x^{\frac{3}{2}} + 8 x^{2}

Solution steps

\frac{( 1 + 2 x ) ^{4}}{2}

(1 + 2 x)^{4} = 1 + 8 x + 24 x + 32 x^{\frac{3}{2}} + 16 x^{2}

= \frac{1 + 8 x + 24 x + 32 x ^{\frac{3}{2}} + 16 x ^{2}}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 + 8 x + 24 x + 32 x ^{\frac{3}{2}} + 16 x ^{2}}{2} = \frac{1}{2} + \frac{8 x}{2} + \frac{24 x}{2} + \frac{32 x ^{\frac{3}{2}}}{2} + \frac{16 x ^{2}}{2}

= \frac{1}{2} + \frac{8 x}{2} + \frac{24 x}{2} + \frac{32 x ^{\frac{3}{2}}}{2} + \frac{16 x ^{2}}{2}

\frac{8 x}{2} = 4 x

\frac{24 x}{2} = 12 x

\frac{32 x ^{\frac{3}{2}}}{2} = 16 x^{\frac{3}{2}}

\frac{16 x ^{2}}{2} = 8 x^{2}

= \frac{1}{2} + 4 x + 12 x + 16 x^{\frac{3}{2}} + 8 x^{2}

(1 + 2 e^{i t})^{3}

5 sec (\frac{π}{4} (x + 1))

\frac{18}{23} - \frac{1}{23}

\frac{x ( - x y ^{2} - x ^{2} y + 32 x )}{( y + x ) ^{2}}

(1 + 0.9 z) \cdot (1 - 0, 9 z) \cdot (1 + 2 z)

What is expand ((1+2sqrt(x))^4)/2 ?
The solution to expand ((1+2sqrt(x))^4)/2 is 1/2+4sqrt(x)+12x+16x^{3/2}+8x^2