Question

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

$(3x+5y{)}^3$

Short answer

Expansion is$27x^3+135x^{2}y+225x{y}^2+125y^3$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

$(3x+5y{)}^3$

Solution

We have

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

The expansion is

$$\begin{gathered} (3x+5y{)}^3=1(3x{)}^3+3(3x{)}^2\left(5y\right)+3(3x\left)\right(5y{)}^2+1(5y{)}^3 \\ =27x^3+135x^{2}y+225x{y}^2+125y^3 \end{gathered}$$