Find the indicated coefficient or term.
-The coefficient of $x ^ { 8 }$ in the expansion of $\left( x ^ { 2 } - 3 \right) ^ { 7 }$
A) 945
B) -945
C) 2835
D) -2835

Question

Quizplus · Accepted Answer

The coefficient of $x^8$ in the expansion of $(x^2 - 3)^7$ can be found using the binomial theorem. The general term in the expansion of $(a + b)^n$ is given by $\binom{n}{k}a^{n-k}b^k$, where $\binom{n}{k}$ is the binomial coefficient. For $x^8$, we need the term where $x^2$ is raised to the 4th power (since $2 \times 4 = 8$), meaning $k = 4$. Thus, the coefficient is $\binom{7}{4}(-3)^{7-4} = \binom{7}{4}(-3)^3 = 35 \times (-27) = -945$.

Find the Indicated Coefficient or Term x8x ^ { 8 }x8

Find the Indicated Coefficient or Term $x ^ { 8 }$