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

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

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

expand

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

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

Solution steps

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

(x^{2} + x + 1)^{2} = x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

- \frac{2 x}{( x ^{2} + c ) ^{2}}

(x - y = 5,) (x + 2 y = 7)

\frac{x}{( x - 2 ) ( x - 3 ) ( s - 6 )}

\frac{( 4 x - 1000 ) ^{2}}{9}

e^{2 x} (2 x e^{2 x} + e^{2 x})

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