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Find the coefficient of x^5 in the product (1+2x)^6(1-x)^7 ?
(1+2x)6 (1-x)7=[1+6C1(2x)+6C2(2X)2+6C3(2X)3+6C4(2X)4+6C5(2X)5+6C6(2X)6 ][1-7C1.X+7C2.X2-7C3.X3+7C4.X4-7C5.X5+7C6.X6-7C7.X7] Hence coefficient of x5= -7c5+7c4.6c1(2)-7c3.6c2.22+7c2.6c3.23-7c1.6c4.24+6c5.25 =-21+420-2100+3360-1680+192 =3972-3801 =171Thanks & RegardsRinkoo GuptaAskIITians Faculty
(1+2x)6 (1-x)7=[1+6C1(2x)+6C2(2X)2+6C3(2X)3+6C4(2X)4+6C5(2X)5+6C6(2X)6 ][1-7C1.X+7C2.X2-7C3.X3+7C4.X4-7C5.X5+7C6.X6-7C7.X7]
Hence coefficient of x5= -7c5+7c4.6c1(2)-7c3.6c2.22+7c2.6c3.23-7c1.6c4.24+6c5.25
=-21+420-2100+3360-1680+192
=3972-3801
=171
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
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