Question

Expand using binomial theorem(3a-2)^3

Answer 1

Answer:

Recall that the binomial theorem states that:

$(a+b)^n=\sum ^n_{k=0}{\binom{n}{k}}a^{n-k}b^k\text{.}$

Therefore:

$\mleft(3a-2\mright)^3=\sum ^3_{k=0}{\binom{3}{k}}(3a)^{3-k}(-2)^k.$

Then:

$\begin{gathered} (3a-2)^3={\binom{3}{0}}(3a)^{3-0}(-2)^0+{\binom{3}{1}}(3a)^{3-1}(-2)^1+{\binom{3}{2}}(3a)^{3-2}(-2)^2 \\ +{\binom{3}{3}}(3a)^{3-3}(-2)^3\text{.} \end{gathered}$

Simplifying the above result we get

$\begin{gathered} (3a-2)^3=(3a)^3+3(3a)^2(-2)+3(3a)(-2)^2+(-2)^3 \\ =27a^3-54a^2+36a-8. \end{gathered}$