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+⁷c₂.⁶c_3.2³-⁷c₁.⁶c₄.2⁴+⁶c_5.2⁵

^{=-21+420-2100+3360-1680+192}

^=3972-3801

⁼¹⁷¹

^{Thanks & Regards}

^{Rinkoo Gupta}

^{AskIITians Faculty}