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Question

Find the coefficient of a4 in the product (1+2a)4(2a)5 using binomial theorem.

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Solution

(1+2a)^4$
4C1+4C1(2a)+4C2(2a)2+4C3(2a)3+4C4(2a)4
1+8a+24a2+32a3+16a4
(2a)5
5C0255C124(a)+5C223(a)25C322a3+5C42a45C5a5
3280a+80a3+10a4a5
Coefficient of a4 is 1×10a4+(8a)(80a3)+32a3(80a)+16a4(32)
10a4+640a42560a4+512a4
1.398x4.

1043068_1040863_ans_146f97e9c0a64606acb8cb58bcf6e0f0.jpg

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