What is expand 1/4 ((s+2)^2(s-2)^3(s^2+4)) ?

The solution to expand 1/4 ((s+2)^2(s-2)^3(s^2+4)) is (s^7)/4-(s^6)/2-s^5+2s^4-4s^3+8s^2+16s-32

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expand 1/4 ((s+2)^2(s-2)^3(s^2+4))

expand

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

\frac{s ^{7}}{4} - \frac{s ^{6}}{2} - s^{5} + 2 s^{4} - 4 s^{3} + 8 s^{2} + 16 s - 32

Solution steps

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

Remove parentheses:

(a) = a

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

Multiply fractions:

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

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

Expand

\frac{1 \cdot ( s + 2 ) ^{2} ( s - 2 ) ^{3}}{4} : \frac{s ^{5} - 2 s ^{4} - 8 s ^{3} + 16 s ^{2} + 16 s - 32}{4}

= \frac{s ^{5} - 2 s ^{4} - 8 s ^{3} + 16 s ^{2} + 16 s - 32}{4} (s^{2} + 4)

Multiply fractions:

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

= \frac{( s ^{5} - 2 s ^{4} - 8 s ^{3} + 16 s ^{2} + 16 s - 32 ) ( s ^{2} + 4 )}{4}

Expand

(s^{5} - 2 s^{4} - 8 s^{3} + 16 s^{2} + 16 s - 32) (s^{2} + 4) : s^{7} - 2 s^{6} - 4 s^{5} + 8 s^{4} - 16 s^{3} + 32 s^{2} + 64 s - 128

= \frac{s ^{7} - 2 s ^{6} - 4 s ^{5} + 8 s ^{4} - 16 s ^{3} + 32 s ^{2} + 64 s - 128}{4}

Apply the fraction rule:

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

\frac{s ^{7} - 2 s ^{6} - 4 s ^{5} + 8 s ^{4} - 16 s ^{3} + 32 s ^{2} + 64 s - 128}{4} = \frac{s ^{7}}{4} - \frac{2 s ^{6}}{4} - \frac{4 s ^{5}}{4} + \frac{8 s ^{4}}{4} - \frac{16 s ^{3}}{4} + \frac{32 s ^{2}}{4} + \frac{64 s}{4} - \frac{128}{4}

= \frac{s ^{7}}{4} - \frac{2 s ^{6}}{4} - \frac{4 s ^{5}}{4} + \frac{8 s ^{4}}{4} - \frac{16 s ^{3}}{4} + \frac{32 s ^{2}}{4} + \frac{64 s}{4} - \frac{128}{4}

\frac{2 s ^{6}}{4} = \frac{s ^{6}}{2}

\frac{4 s ^{5}}{4} = s^{5}

\frac{8 s ^{4}}{4} = 2 s^{4}

\frac{16 s ^{3}}{4} = 4 s^{3}

\frac{32 s ^{2}}{4} = 8 s^{2}

\frac{64 s}{4} = 16 s

\frac{128}{4} = 32

= \frac{s ^{7}}{4} - \frac{s ^{6}}{2} - s^{5} + 2 s^{4} - 4 s^{3} + 8 s^{2} + 16 s - 32

10 - 10 e^{- 3 x} (cos (3 x) + sin (3 x))

(- 4) \cdot 8 a + 16

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

24 x^{2} - 10 x - 3 (y + x \frac{d y}{d x})

\frac{n ^{4} - 2 n ^{3} + 0 n ^{2} + 2 n - 1}{n ^{2} - 2 n + 1}

What is expand 1/4 ((s+2)^2(s-2)^3(s^2+4)) ?
The solution to expand 1/4 ((s+2)^2(s-2)^3(s^2+4)) is (s^7)/4-(s^6)/2-s^5+2s^4-4s^3+8s^2+16s-32