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}

π (- 2 sin (π y) + π cos (π y))

\frac{- 1}{3} (2 y - 9 = - 2)

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

\frac{( 9 a + 1 ) ^{3}}{27}

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

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