Chapter 13.8, Problem 66HP

To determine

Expand the terms of the expression.

Answer to Problem 66HP

The expansion is $a^4+b^4+6a^2{b}^2-4a{b}^3-4a^{3}b$ .

Explanation of Solution

Given:

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

Concept Used:

In this, use the concept of expanding the term and also use the formula of ${(a-b)}^2=a^2+b^2+2ab,$

  ${(a+b+c)}^2=a^2+b^2+2ab+2bc+2ca+c^2$ .

Calculation:

Here,

  $\begin{array}{l}$ {(a-b)}^4$$ {\left\{{(a-b)}^2\right\}}^2$$ {(a^2+b^2-2ab)}^2$$ {[a^2+b^2+(-2ab)]}^2$a^4+b^4+4a^2{b}^2+2a^2{b}^2+2\times b^2\times -2ab+2\times -2ab\times a^2\\ a^4+b^4+6a^2{b}^2-4a{b}^3-4a^{3}b\end{array}$

Conclusion:

The option is D i.e. $a^4+b^4+6a^2{b}^2-4a{b}^3-4a^{3}b$ .