What is expand ((2+x^2+2x^3)^2)/4 ?

The solution to expand ((2+x^2+2x^3)^2)/4 is x^6+x^5+(x^4)/4+2x^3+x^2+1

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expand ((2+x^2+2x^3)^2)/4

expand

\frac{( 2 + x ^{2} + 2 x ^{3} ) ^{2}}{4}

x^{6} + x^{5} + \frac{x ^{4}}{4} + 2 x^{3} + x^{2} + 1

Solution steps

\frac{( 2 + x ^{2} + 2 x ^{3} ) ^{2}}{4}

(2 + x^{2} + 2 x^{3})^{2} = 8 x^{3} + 4 x^{5} + 4 x^{6} + 4 x^{2} + x^{4} + 4

= \frac{8 x ^{3} + 4 x ^{5} + 4 x ^{6} + 4 x ^{2} + x ^{4} + 4}{4}

Apply the fraction rule:

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

\frac{8 x ^{3} + 4 x ^{5} + 4 x ^{6} + 4 x ^{2} + x ^{4} + 4}{4} = \frac{8 x ^{3}}{4} + \frac{4 x ^{5}}{4} + \frac{4 x ^{6}}{4} + \frac{4 x ^{2}}{4} + \frac{x ^{4}}{4} + \frac{4}{4}

= \frac{8 x ^{3}}{4} + \frac{4 x ^{5}}{4} + \frac{4 x ^{6}}{4} + \frac{4 x ^{2}}{4} + \frac{x ^{4}}{4} + \frac{4}{4}

Apply rule

\frac{a}{a} = 1

\frac{4}{4} = 1

= \frac{8 x ^{3}}{4} + \frac{4 x ^{5}}{4} + \frac{4 x ^{6}}{4} + \frac{4 x ^{2}}{4} + \frac{x ^{4}}{4} + 1

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

\frac{4 x ^{5}}{4} = x^{5}

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

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

= 2 x^{3} + x^{5} + x^{6} + x^{2} + \frac{x ^{4}}{4} + 1

Rewrite in standard form

= x^{6} + x^{5} + \frac{x ^{4}}{4} + 2 x^{3} + x^{2} + 1

\frac{2}{3} (6 x - 15 = 18)

\frac{1}{2 ( - 28 - 16 a )}

\frac{x ^{2} + 148}{( x - 6 ) ( x + 8 )}

\frac{( z + 2 ) ( z + 6 )}{z + 3}

20 (31)

What is expand ((2+x^2+2x^3)^2)/4 ?
The solution to expand ((2+x^2+2x^3)^2)/4 is x^6+x^5+(x^4)/4+2x^3+x^2+1