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

The solution to expand ((1+2sqrt(x))^4)/4 is 1/4+2sqrt(x)+6x+8x^{3/2}+4x^2

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

expand

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

\frac{1}{4} + 2 x + 6 x + 8 x^{\frac{3}{2}} + 4 x^{2}

Solution steps

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

(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}}{4}

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

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

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

\frac{24 x}{4} = 6 x

\frac{32 x ^{\frac{3}{2}}}{4} = 8 x^{\frac{3}{2}}

\frac{16 x ^{2}}{4} = 4 x^{2}

= \frac{1}{4} + 2 x + 6 x + 8 x^{\frac{3}{2}} + 4 x^{2}

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What is expand ((1+2sqrt(x))^4)/4 ?
The solution to expand ((1+2sqrt(x))^4)/4 is 1/4+2sqrt(x)+6x+8x^{3/2}+4x^2