By binomial theorem
(x+y)n=∑k=0n(nk)xn−kyk=∑k=0nn!(n−k)!k!xn−kykax2=6!(6−2)!2!34(−2x)2=4860x2bx3=6!(6−3)!3!33(−2x)3=−4320x3ab=4860−4320=−1.125(x+y)^n=\sum\limits_{k=0}^{n}\begin{pmatrix} n \\ k \end{pmatrix}x^{n-k}y^k=\\ \sum\limits_{k=0}^{n}\cfrac{n!}{(n-k)!k!}x^{n-k}y^k\\ ax^2=\cfrac{6!}{(6-2)!2!}3^{4}(-2x)^2=4860x^2\\ bx^3=\cfrac{6!}{(6-3)!3!}3^{3}(-2x)^3=-4320x^3\\ \cfrac{a}{b}=\cfrac{4860}{-4320}=-1.125(x+y)n=k=0∑n(nk)xn−kyk=k=0∑n(n−k)!k!n!xn−kykax2=(6−2)!2!6!34(−2x)2=4860x2bx3=(6−3)!3!6!33(−2x)3=−4320x3ba=−43204860=−1.125
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