Find the coefficient, C, of the term in the binomial expansion.
Binomial: (4x - 3y) ⁴ Term: Cxy³

Question

Find the coefficient, C, of the term in the binomial expansion. Binomial: (4x - 3y)⁴ Term: Cxy³ A) 432 B) -432 C) 108 D) -108

Quizplus · Accepted Answer

The coefficient, C, of the term $xy^{13}$ in the expansion of $(4x - 3y)^{14}$ can be found using the binomial theorem, which in general form is $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. For the term $xy^{13}$, $n=14$, $k=13$, $a=4x$, and $b=-3y$. Thus, the coefficient is $\binom{14}{13} (4x)^{14-13}(-3y)^{13} = 14 \cdot 4 \cdot (-3)^{13}$. Calculating this gives $-432$, as the negative sign comes from the odd power of -3.

Find the Coefficient, C, of the Term in the Binomial