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

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

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

expand

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

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

Solution steps

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

Expand

(- x + 2)^{2} : x^{2} - 4 x + 4

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

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

Expand

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

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

Expand

(x^{2} + 2 x + 1) (x^{2} - 4 x + 4) : x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 4

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

Distribute parentheses

= \frac{- 1}{4} x^{4} + \frac{- 1}{4} (- 2 x^{3}) + \frac{- 1}{4} (- 3 x^{2}) + \frac{- 1}{4} \cdot 4 x + \frac{- 1}{4} \cdot 4

Simplify

\frac{- 1}{4} x^{4} + \frac{- 1}{4} (- 2 x^{3}) + \frac{- 1}{4} (- 3 x^{2}) + \frac{- 1}{4} \cdot 4 x + \frac{- 1}{4} \cdot 4 : - \frac{x ^{4}}{4} + \frac{x ^{3}}{2} + \frac{3 x ^{2}}{4} - x - 1

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

(1 - 3 x) (x + 2)^{'}

2 t (2 t - 2)

[(x + 1) (x - 1)] 2

(- t^{3} + \frac{9}{10} t + \frac{1}{10}) (1 + t + t^{2})

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

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