What is expand (2+1/4 x)^8(4x^2-12+9/(x^2)) ?

The solution to expand (2+1/4 x)^8(4x^2-12+9/(x^2)) is

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expand (2+1/4 x)^8(4x^2-12+9/(x^2))

expand

(2 + \frac{1}{4} x)^{8} (4 x^{2} - 12 + \frac{9}{x ^{2}})

- 320 x^{2} + 688 x^{3} + \frac{791 x ^{4}}{2} + \frac{427 x ^{5}}{4} + \frac{1099 x ^{6}}{64} + \frac{445 x ^{7}}{256} + \frac{1789 x ^{8}}{16384} + \frac{x ^{9}}{256} + \frac{x ^{10}}{16384} - 3072 - 3072 x + \frac{9 ( 2 + \frac{1}{4} x ) ^{8}}{x ^{2}}

Solution steps

(2 + \frac{1}{4} x)^{8} (4 x^{2} - 12 + \frac{9}{x ^{2}})

Apply the distributive law:

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

(2 + \frac{1}{4} x)^{8} (4 x^{2} - 12 + \frac{9}{x ^{2}}) = (2 + \frac{1}{4} x)^{8} \cdot 4 x^{2} + (2 + \frac{1}{4} x)^{8} (- 12) + (2 + \frac{1}{4} x)^{8} \frac{9}{x ^{2}}

= (2 + \frac{1}{4} x)^{8} \cdot 4 x^{2} + (2 + \frac{1}{4} x)^{8} (- 12) + (2 + \frac{1}{4} x)^{8} \frac{9}{x ^{2}}

Simplify

(2 + \frac{1}{4} x)^{8} \cdot 4 x^{2} + (2 + \frac{1}{4} x)^{8} (- 12) + (2 + \frac{1}{4} x)^{8} \frac{9}{x ^{2}} : - 320 x^{2} + 688 x^{3} + \frac{791 x ^{4}}{2} + \frac{427 x ^{5}}{4} + \frac{1099 x ^{6}}{64} + \frac{445 x ^{7}}{256} + \frac{1789 x ^{8}}{16384} + \frac{x ^{9}}{256} + \frac{x ^{10}}{16384} - 3072 - 3072 x + \frac{9 ( 2 + \frac{1}{4} x ) ^{8}}{x ^{2}}

= - 320 x^{2} + 688 x^{3} + \frac{791 x ^{4}}{2} + \frac{427 x ^{5}}{4} + \frac{1099 x ^{6}}{64} + \frac{445 x ^{7}}{256} + \frac{1789 x ^{8}}{16384} + \frac{x ^{9}}{256} + \frac{x ^{10}}{16384} - 3072 - 3072 x + \frac{9 ( 2 + \frac{1}{4} x ) ^{8}}{x ^{2}}

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

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

\frac{x + 1}{5 ( x + 2 )}

3 (10 - 6 y + e^{- 3 x})

4 t (x) x^{^{''}} + (t (x) - 8) x^{^{'}} - x

What is expand (2+1/4 x)^8(4x^2-12+9/(x^2)) ?
The solution to expand (2+1/4 x)^8(4x^2-12+9/(x^2)) is