Question

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

$(p+q{)}^9$

Short answer

The expansion is$p^9+9p^{8}q+36p^7{q}^2+84p^6{q}^3+126p^5{q}^4+126p^4{q}^5+84p^3{q}^6+36p^2{q}^7+9p{q}^8+q^9$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

$(p+q{)}^9$

Solution

We have

The exponent is 9 hence tenth row need to be considered

The expansion is

$$\begin{gathered} (p+q{)}^9=1p^9+9p^{8}q+36p^7{q}^2+84p^6{q}^3+126p^5{q}^4+126p^4{q}^5+84p^3{q}^6+36p^2{q}^7+9p{q}^8+1q^9 \\ =p^9+9p^{8}q+36p^7{q}^2+84p^6{q}^3+126p^5{q}^4+126p^4{q}^5+84p^3{q}^6+36p^2{q}^7+9p{q}^8+q^9 \end{gathered}$$