Find the coefficient of the $x^3$ term in the expansion of $(x – 2)^{10}$.
Question Q7
Find the coefficient of the $x^3$ term in the expansion of $(x – 2)^{10}$.
Mark Scheme
General term is $inom{n}{r} a^{n-r} b^r$. Here $n=10, a=x, b=-2$.
We want $x^3$, so we need $n-r = 3$, which means $10-r=3$, so $r=7$.
Term = $inom{10}{7} (x)^3 (-2)^7$
$inom{10}{7} = frac{10 imes 9 imes 8}{3 imes 2 imes 1} = 120$.
$(-2)^7 = -128$.
Coefficient = $120 imes (-128) = -15360$.
