Find the coefficient of \(\displaystyle x^5\) in \(\displaystyle (3 - 4x)(2x+3)^7\)

**My solution**

So I started off by separating both brackets into 2 separate equations.

1. \(\displaystyle 3(2x+3)^7\)

2. \(\displaystyle -4x(2x+3)^7\)

**Now I find the coefficient of**\(\displaystyle x^5\)

**in equation 1 and I find the coefficient of**\(\displaystyle x^4\)

**in equation 2.**

So now:

1. \(\displaystyle 3 \binom{7}{5}\) \(\displaystyle (3)^2\) \(\displaystyle (2)^5\) = \(\displaystyle 3 \times 21 \times 9 \times 32\)

2. \(\displaystyle -4 \binom{7}{4}\) \(\displaystyle (3)^3\) \(\displaystyle (2)^4\) = \(\displaystyle -4 \times 35 \times 27 \times 16\)

So now adding both up:

Solution: \(\displaystyle 3 \times 21 \times 9 \times 32 - 4 \times 35 \times 27 \times 16\)