What is expand 1/2-((w-1)^2)/2+2w-2-(w^2-1)/2 ?

The solution to expand 1/2-((w-1)^2)/2+2w-2-(w^2-1)/2 is -w^2+3w+1/2-2

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expand 1/2-((w-1)^2)/2+2w-2-(w^2-1)/2

expand

\frac{1}{2} - \frac{( w - 1 ) ^{2}}{2} + 2 w - 2 - \frac{w ^{2} - 1}{2}

- w^{2} + 3 w + \frac{1}{2} - 2

Solution steps

\frac{1}{2} - \frac{( w - 1 ) ^{2}}{2} + 2 w - 2 - \frac{w ^{2} - 1}{2}

Combine the fractions

\frac{1}{2} - \frac{( w - 1 ) ^{2}}{2} - \frac{w ^{2} - 1}{2} : \frac{1 - ( w - 1 ) ^{2} - ( w ^{2} - 1 )}{2}

= \frac{1 - ( w - 1 ) ^{2} - ( w ^{2} - 1 )}{2} + 2 w - 2

Expand

1 - (w - 1)^{2} - (w^{2} - 1) : - 2 w^{2} + 2 w + 1

= \frac{- 2 w ^{2} + 2 w + 1}{2} + 2 w - 2

Combine the fractions

\frac{- 2 w ^{2} + 2 w + 1}{2} + 2 w : \frac{- 2 w ^{2} + 6 w + 1}{2}

= \frac{- 2 w ^{2} + 6 w + 1}{2} - 2

Apply the fraction rule:

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

\frac{- 2 w ^{2} + 6 w + 1}{2} = - \frac{2 w ^{2}}{2} + \frac{6 w}{2} + \frac{1}{2}

= - \frac{2 w ^{2}}{2} + \frac{6 w}{2} + \frac{1}{2} - 2

Divide the numbers:

\frac{2}{2} = 1

= - w^{2} + \frac{6 w}{2} + \frac{1}{2} - 2

Divide the numbers:

\frac{6}{2} = 3

= - w^{2} + 3 w + \frac{1}{2} - 2

(2 (n - 1))!

(- 2 sin (t))^{2} + (2 cos (t))^{2} + (4 cos (t) - 2 sin (t))^{2}

\frac{1}{( n - 1 ) ^{2}} + \frac{1}{n - 1} - \frac{1}{n}

(9 + cos (θ))^{3}

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

What is expand 1/2-((w-1)^2)/2+2w-2-(w^2-1)/2 ?
The solution to expand 1/2-((w-1)^2)/2+2w-2-(w^2-1)/2 is -w^2+3w+1/2-2