What is expand 1/2 (x-3)^2(x+1)^3 ?

The solution to expand 1/2 (x-3)^2(x+1)^3 is (x^5)/2-(3x^4)/2-3x^3+5x^2+(21x)/2+9/2

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expand 1/2 (x-3)^2(x+1)^3

expand

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

\frac{x ^{5}}{2} - \frac{3 x ^{4}}{2} - 3 x^{3} + 5 x^{2} + \frac{21 x}{2} + \frac{9}{2}

Solution steps

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

Expand

(x - 3)^{2} : x^{2} - 6 x + 9

= \frac{1}{2} (x^{2} - 6 x + 9) (x + 1)^{3}

= \frac{1}{2} (x + 1)^{3} (x^{2} - 6 x + 9)

Expand

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

= \frac{1}{2} (x^{3} + 3 x^{2} + 3 x + 1) (x^{2} - 6 x + 9)

Expand

(x^{3} + 3 x^{2} + 3 x + 1) (x^{2} - 6 x + 9) : x^{5} - 3 x^{4} - 6 x^{3} + 10 x^{2} + 21 x + 9

= \frac{1}{2} (x^{5} - 3 x^{4} - 6 x^{3} + 10 x^{2} + 21 x + 9)

Distribute parentheses

= \frac{1}{2} x^{5} + \frac{1}{2} (- 3 x^{4}) + \frac{1}{2} (- 6 x^{3}) + \frac{1}{2} \cdot 10 x^{2} + \frac{1}{2} \cdot 21 x + \frac{1}{2} \cdot 9

Simplify

\frac{1}{2} x^{5} + \frac{1}{2} (- 3 x^{4}) + \frac{1}{2} (- 6 x^{3}) + \frac{1}{2} \cdot 10 x^{2} + \frac{1}{2} \cdot 21 x + \frac{1}{2} \cdot 9 : \frac{x ^{5}}{2} - \frac{3 x ^{4}}{2} - 3 x^{3} + 5 x^{2} + \frac{21 x}{2} + \frac{9}{2}

= \frac{x ^{5}}{2} - \frac{3 x ^{4}}{2} - 3 x^{3} + 5 x^{2} + \frac{21 x}{2} + \frac{9}{2}

\frac{4}{( s + 2 ) ^{2}}

\frac{( e ^{- s} + s ^{2} + s + 10 )}{( s + 4 ) ( s - 2 ) ( s - 1 )}

\frac{s ^{2} + 9 s + 10}{( s + 1 ) ( s ^{2} + 5 s + 6 )}

b (6 - \frac{b ^{2}}{4})

What is expand 1/2 (x-3)^2(x+1)^3 ?
The solution to expand 1/2 (x-3)^2(x+1)^3 is (x^5)/2-(3x^4)/2-3x^3+5x^2+(21x)/2+9/2