Question

In the following exercises, expand each binomial using Pascal's Triangle.

$(2x+3y{)}^3$

Short answer

Expansion is$8x^3+36x^{2}y+54x{y}^2+27y^3$

Step-by-step solution

Step 1. Given Information

Expand binomial using Pascal's Triangle.

$(2x+3y{)}^3$

Step 2. Solution

We have

Here the exponent is 3 hence we need to consider fourth row

The expansion is

$$\begin{gathered} (2x+3y{)}^3=1(2x{)}^3+3(2x{)}^2\left(3y\right)+3(2x\left)\right(3y{)}^2+1(3y{)}^3 \\ =8x^3+36x^{2}y+54x{y}^2+27y^3 \end{gathered}$$