Question

Expand: (3a - 4b)^8. Write a brief explanation of your process for finding the expansion of this binomial.

Answer 1

To expand the binomial

$(3a-4b)^8$

We can use the binomial theorem.

According to the binomial theorem, our binomial can be rewritten as:

$(3a-4b)^8=\sum_{n\mathop{=}0}^8\begin{pmatrix}8 \\ n\end{pmatrix}(3a)^{8-n}(-4b)^n$

Then, expanding this sum, we have:

$\begin{gathered} (3a-4b)^8=\frac{8!}{0!(8-0)!}(3a)^8(-4b)^0+\frac{8!}{1!(8-1)!}(3a)^7(-4b)^1+... \\ +\frac{8!}{7!(8-7)!}(3a)^1(-4b)^7+\frac{8!}{8!(8-8)!}(3a)^0(-4b)^8 \\ \\ =6561a^8-69984a^7b-870912a^5b^3+1451520a^4b^4-1548288a^3b^5 \\ +1032192a^2b^6-393216ab^7+65536b^8 \end{gathered}$