Find a Particular Term in a Binomial Expansion
-$( x - 3 ) ^ { 17 }$
A) $x 17 - 51 \times 16 + 1224 \times 15$
B) $x ^ { 17 } - 51 \times 16 - 1224 \times 15$
C) $\times 17 + 51 \times 16 + 1224 \times 15$
D) $x 17 + 51 \times 16 - 1224 \times 15$

Question

Quizplus · Accepted Answer

The correct term is derived from the binomial expansion formula, which for a term $t_{r+1}$ in the expansion of $(x + y)^n$ is given by $\binom{n}{r} x^{n-r}y^r$. For the term involving $x^{17}$, $r=0$, so the term is simply $x^{17}$ as there's no $y$ component (in this case, $y = -3$), and the coefficients for subsequent terms involve combinations and powers of -3, which are not relevant for the $x^{17}$ term.

Find a Particular Term in a Binomial Expansion - (x−3)17( x - 3 ) ^ { 17 }(x−3)17

Find a Particular Term in a Binomial Expansion
- $( x - 3 ) ^ { 17 }$