Question

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

$(x+y{)}^4$

Short answer

Expansion is$x^4+4x^{3}y+6x^2{y}^2+4x{y}^3+y^4$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

$(x+y{)}^4$

Step 2. Calculation

We have

The exponent is 4 hence fifth row need to be considered

The expansion is

$\begin{array}{rcl}(x+y{)}^4& =& 1x^4+4x^{3}y+6x^2{y}^2+4x{y}^3+1y^4\\ & =& x^4+4x^{3}y+6x^2{y}^2+4x{y}^3+y^4\end{array}$