What is expand (1+7/2 x)(2-9x)^4 ?

The solution to expand (1+7/2 x)(2-9x)^4 is -13851x^4+972x^3+936x^2-232x+(45927x^5)/2+16

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expand (1+7/2 x)(2-9x)^4

expand

(1 + \frac{7}{2} x) (2 - 9 x)^{4}

- 13851 x^{4} + 972 x^{3} + 936 x^{2} - 232 x + \frac{45927 x ^{5}}{2} + 16

Solution steps

(1 + \frac{7}{2} x) (2 - 9 x)^{4}

= (2 - 9 x)^{4} (1 + \frac{7}{2} x)

Apply the distributive law:

a (b + c) = ab + a c

(2 - 9 x)^{4} (1 + \frac{7}{2} x) = (2 - 9 x)^{4} \cdot 1 + (2 - 9 x)^{4} \frac{7}{2} x

= (2 - 9 x)^{4} \cdot 1 + (2 - 9 x)^{4} \frac{7}{2} x

Apply rule:

a \cdot 1 = a

(2 - 9 x)^{4} \cdot 1 = (2 - 9 x)^{4}

= (2 - 9 x)^{4} + (2 - 9 x)^{4} \frac{7}{2} x

= (2 - 9 x)^{4} + \frac{7}{2} x (2 - 9 x)^{4}

Expand

(2 - 9 x)^{4} : 16 - 288 x + 1944 x^{2} - 5832 x^{3} + 6561 x^{4}

= 16 - 288 x + 1944 x^{2} - 5832 x^{3} + 6561 x^{4} + \frac{7}{2} x (2 - 9 x)^{4}

Expand

\frac{7}{2} x (2 - 9 x)^{4} : 56 x - 1008 x^{2} + 6804 x^{3} - 20412 x^{4} + \frac{45927 x ^{5}}{2}

= 16 - 288 x + 1944 x^{2} - 5832 x^{3} + 6561 x^{4} + 56 x - 1008 x^{2} + 6804 x^{3} - 20412 x^{4} + \frac{45927 x ^{5}}{2}

Simplify

16 - 288 x + 1944 x^{2} - 5832 x^{3} + 6561 x^{4} + 56 x - 1008 x^{2} + 6804 x^{3} - 20412 x^{4} + \frac{45927 x ^{5}}{2} : - 13851 x^{4} + 972 x^{3} + 936 x^{2} - 232 x + \frac{45927 x ^{5}}{2} + 16

= - 13851 x^{4} + 972 x^{3} + 936 x^{2} - 232 x + \frac{45927 x ^{5}}{2} + 16

\frac{3 x ^{2} - 11 x - 98}{( x ^{2} - 4 ) ( x + 1 )}

(sin (x^{2}) + 5)^{2}

(1 - 4 sin^{2} (b)) cos (b)

(2 x + 2 y) (x + y) cos (x^{2} + 2 x y + y^{2})

\frac{t ( x ^{2} + 2 x )}{( x + 1 )}

What is expand (1+7/2 x)(2-9x)^4 ?
The solution to expand (1+7/2 x)(2-9x)^4 is -13851x^4+972x^3+936x^2-232x+(45927x^5)/2+16