Question

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

$(a+b{)}^8$

Short answer

Expansion is$a^8+8a^{7}b+28a^6{b}^2+56a^5{b}^3+70a^4{b}^4+56a^3{b}^5+28a^2{b}^6+8a{b}^7+b^8$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

$(a+b{)}^8$

Solution

We have

Here the exponent is 8 hence we need to consider ninth row

The expansion is

$$\begin{gathered} (a+b{)}^8=1a^8+8a^{7}b+28a^6{b}^2+56a^5{b}^3+70a^4{b}^4+56a^3{b}^5+28a^2{b}^6+8a{b}^7+1b^8 \\ =a^8+8a^{7}b+28a^6{b}^2+56a^5{b}^3+70a^4{b}^4+56a^3{b}^5+28a^2{b}^6+8a{b}^7+b^8 \end{gathered}$$