Question

Find the following expression by multiplying (A+b)^3

Answer 1

Given expression: (A+b)^3.

We can expand it into three factors as (A+b)(A+b)(A+b).

First we would foil (A+b)(A+b) = $A^2 + Ab+Ab+ b^2$

Combining like terms, we get

= $A^2 +2Ab + b^2$

Now, we would multiply (A^2 +2Ab + b^2) and (A+b).

=$A^3 + A^2b + 2A^2b+2Ab^2 + Ab^2+ b^3$

Combining like terms, we get

$=A^3+3A^2b+3Ab^2+b^3$

Therefore,

$\left(A+b\right)^3=\quad A^3+3A^2b+3Ab^2+b^3$