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

The solution to expand (x^2+4)^2*((x-1)/2) is ((x-1)x^4)/2+4x^3-4x^2+8x-8

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

expand

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

\frac{( x - 1 ) x ^{4}}{2} + 4 x^{3} - 4 x^{2} + 8 x - 8

Solution steps

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

Apply rule:

(a) = a

(\frac{x - 1}{2}) = \frac{x - 1}{2}

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

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

Expand

(x^{2} + 4)^{2} : x^{4} + 8 x^{2} + 16

= \frac{x - 1}{2} (x^{4} + 8 x^{2} + 16)

Apply the distributive law:

m (a + b + c) = ma + mb + m c

\frac{x - 1}{2} (x^{4} + 8 x^{2} + 16) = \frac{x - 1}{2} x^{4} + \frac{x - 1}{2} \cdot 8 x^{2} + \frac{x - 1}{2} \cdot 16

= \frac{x - 1}{2} x^{4} + \frac{x - 1}{2} \cdot 8 x^{2} + \frac{x - 1}{2} \cdot 16

Simplify

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

= \frac{( x - 1 ) x ^{4}}{2} + 4 x^{3} - 4 x^{2} + 8 x - 8

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

\frac{x ^{2} + 6 x + 5}{( x - 1 ) ( 2 x + 1 )}

\frac{9 ( 253 + 64018 )}{2}

\frac{22 ( 27 s + 1 )}{27 s}

\frac{5 \cdot 2 + 17}{7}

What is expand (x^2+4)^2*((x-1)/2) ?
The solution to expand (x^2+4)^2*((x-1)/2) is ((x-1)x^4)/2+4x^3-4x^2+8x-8