Find the coefficient of `a^4` in the product `(1+2a)^4(2-a)^5` using binomial theorem.

Explanation

Given

`(1+2 a)^{4}(2-a)^{5}`

`=[\ ^{4} C_{0}(2 a)^{0}+\ ^{4} C_{1}(2 a)^{1}+\ ^{4} C_{2}(2 a)^{2}+\ ^{4} C_{3}(2 a)^{3}+\ ^{4} C_{4}(2 a)^{4}] times`

`[\ ^{5} C_{0}(2)^{5}(-a)^{0}+\ ^{5} C_{1}(2)^{4}(-a)^{1}+\ ^{5} C_{2}(2)^{3}(-a)^{2}+\ ^{5} C_{3}(2)^{2}(-a)^{3}+\ ^{5} C_{4}(2)^{1}(-a)^{4}+\ ^{5} C_{5}(2)^{0}(-a)^{5}] `

`=[1+8 a+24 a^{2}+32 a^{3}+16 a^{4}] times[32-80 a+80 a^{2}-40 a^{3}+10 a^{4}-a^{5}]`

Coefficient of `a^{4}=10-320+1920-2560+512=-438`