Question

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

$(a-b{)}^6$

Short answer

The expansion is$a^6-6a^{5}b+15a^4{b}^2-20a^3{b}^3+15a^2{b}^4-6a{b}^5+b^6$

Step-by-step solution

Given Information

Expand binomial using Pascal's Triangle.

$(a-b{)}^6$

Solution

We have

The exponent is 6 hence seventh row need to be considered

The expansion is

$$\begin{gathered} (a-b{)}^6=1a^6+6a^5(-b)+15a^4{(-b)}^2+20a^3{(-b)}^3+15a^2{(-b)}^4+6a{(-b)}^5+1{(-b)}^6 \\ =a^6-6a^{5}b+15a^4{b}^2-20a^3{b}^3+15a^2{b}^4-6a{b}^5+b^6 \end{gathered}$$