Chapter 13.6, Problem 34E

a.

To determine

To find how do these results compare with the expansion of ${(a+b)}^6$ .

Answer to Problem 34E

  ${(a+b)}^6=a^6+6a^{5}b+15a^4{b}^2+20a^3{b}^3+15a^2{b}^4+6a{b}^5+b^6$ .

Explanation of Solution

Given:

The given expression is ${(a+b)}^6$ .

Calculation:

Step 1: In L1, enter the value of the exponent in this case it is $6$ .

  

Step 2: In L2, enter the combination formula using the power of binomial.

Step 3: The coefficients from the combinations will appear in L2.

So, the final result is

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

b.

To determine

To find out how would you change the expression to find the expression of ${(a+b)}^8$

Answer to Problem 34E

  ${(a+b)}^8=a^8+8a^{7}b+28a^6{b}^2+56a^5{b}^3+70a^4{b}^4+56a^3{b}^5+28a^2{b}^6+8a{b}^7+b^8$ .

Explanation of Solution

Given:

The given expression is ${(a+b)}^8$

Calculation:

Step 1: In L1, enter the value of the exponent in this case it is $8$ .

  

Step 2: In L2, enter the combination formula using the power of binomial.

Step 3: The coefficients from the combinations will appear in L2.

So, the final result is

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