Find a Particular Term in a Binomial Expansion
-$$( x + 6 ) ^ { 20 }$$
A) $x ^ { 20 } + 120 x ^ { 19 } + 6840 \times 18$
B) $x ^ { 20 } + 1140 \times 19 + 6840 \times 18$
C) $x ^ { 20 } + 6840 \times 19 + 6840 \times 18$
D) $x ^ { 20 } + 120 \times 19 - 6840 \times 18$

Question

Quizplus · Accepted Answer

The general term in a binomial expansion $(x + y)^n$ is given by $\binom{n}{r} x^{n-r} y^r$, where $\binom{n}{r}$ is the binomial coefficient. For the term $x^{19}$, $r = 1$, so the coefficient is $\binom{20}{1} = 20$, and the term is $20 \cdot x^{19} \cdot 6^1 = 120x^{19}$. The choices provided do not directly match this calculation, indicating a potential misunderstanding in the question's presentation. However, choice A seems to be the closest, suggesting a typographical error in the question or choices.

Find a Particular Term in a Binomial Expansion - (x+6)20( x + 6 ) ^ { 20 }(x+6)20

Find a Particular Term in a Binomial Expansion
- $( x + 6 ) ^ { 20 }$