Hello jvignacio Originally Posted by

**jvignacio** hey guys, just need to check if my working out and solution is correct.

Find the coefficient of $\displaystyle x^5$ in $\displaystyle (x^4 + 4)(3x-4)^9$

**My solution**

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

1. $\displaystyle x^4(3x-4)^9$

2. $\displaystyle 4(3x-4)^9$

**Now I find the coefficient of** $\displaystyle x$** in equation 1 and I find the coefficient of** $\displaystyle x^5$ **in equation 2.**

So: $\displaystyle \binom{9}{9-i}$ $\displaystyle (3x)^{9-i}$ $\displaystyle (-4)^i$

now:

1. $\displaystyle \binom{9}{8}$ $\displaystyle (3)^8$ $\displaystyle (-4)^1$ = $\displaystyle 9 \times 6561 \times (-4)$

2. $\displaystyle 4 \binom{9}{4}$ $\displaystyle (3)^4$ $\displaystyle (-4)^5$ = $\displaystyle 4 \times 126 \times 81 \times (-1024)$

So now adding both up:

Solution: $\displaystyle 9 \times 6561 \times (-4) + 4 \times 126 \times 81 \times (-1024)$

Your method is fine, but you have found the coefficient of $\displaystyle x^8$ in (1) and $\displaystyle x^4$ in (2).

You need to write the terms the other way around:$\displaystyle \big((-4)+3x\big)^9$

The term in $\displaystyle x^i$ is now:$\displaystyle \binom{9}{9-i}(-4)^{9-i}x^i$

Now you can put $\displaystyle i = 1$ and $\displaystyle 5$ respectively.

Grandad