Chapter 9, Problem 23CLT

To determine

Calculate the expression by expanding the binomial theorem.

Answer to Problem 23CLT

The expression will be $\begin{array}{l}65538b^8-393216a{b}^7+1032192a^2{b}^6-1548288a^3{b}^5+1451520a^4{b}^4-870192a^5{b}^4+326592a^6{b}^2\\ -69984a^{7}b+6561a^6\end{array}$ .

Explanation of Solution

Given:

It is given in the question that the expression is ${(3a-4b)}^8$ .

Concept Used:

In this, use the concept of binomial theorem and also use the formula of ${\displaystyle \sum _{r=0}^n{C}_r^n{(x)}^r}{(y)}^{n-r}$ .

Calculation: Here, the expression is ${(3a-4b)}^8$ .

Make the above expression in binomial expression : ${\displaystyle \sum _{r=0}^8{C}_r^8{(3a)}^r}{(-4b)}^{8-r}$

Now, expand the above expression:

Conclusion:

The expression will be $\begin{array}{l}65538b^8-393216a{b}^7+1032192a^2{b}^6-1548288a^3{b}^5+1451520a^4{b}^4-870192a^5{b}^4+326592a^6{b}^2\\ -69984a^{7}b+6561a^6\end{array}$ .