Question

Find the 6th term in the expansion of (x + 2)9.

Answer 1

Answer:

$4032x^4$

Step-by-step explanation:

Use the 10th row of Pascal's Triangle to get you where you need to be.  You need 10 rows because any polynomial raised to the 9th power has 10 terms.  Those 10 terms are, in order:

1, 9, 36, 84, 126, 126, 84, 36, 9, 1

Setting up for the first 6 terms:

$1(x^9)(2^0)+9(x^8)(2^1)+36(x^7)(2^2)+84(x^6)(2^3)+126(x^5)(2^4)+126(x^4)(2^5)+...$

The 6th term is the last one.  It goes on from there, but I stopped at the 6th term, since that is what you need.

Simplifying gives us:

$126(x^4)(32)$

and multiplying gives us:

$4032x^4$