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Chapter 12: Q35. (page 637)

Find the indicated term of each expansion.
Third term of ${(x + y)}^{8}$

Short Answer

Expert verified

The third term of the expansion is $T_{3} = 28 x^{6} y^{2}$

Step by step solution

01

Step 1. Given Information.

Given, binomial expansion is ${(x + y)}^{8}$ and the third term of the expansion is to be determined.

02

Step 2. Calculation.

The general term of the binomial expansion ${(a + b)}^{n}$ is given by:

$T_{r + 1} = \frac{n!}{(n - r)! r!} a^{n - r} b^{r}$

Here n=8, a = x, b = y and r + 1 = 3.

Plugging the values:

$\begin{array}{l} T_{r + 1} = \frac{n!}{(n 鈭� r)! r!} a^{n 鈭� r} b^{r} \\ T_{3} = \frac{8!}{(8 鈭� 2)! 2!} x^{8 鈭� 2} y^{2} \\ T_{3} = \frac{8!}{6! 2!} x^{6} y^{2} \\ T_{3} = 28 x^{6} y^{2} \end{array}$

03

Step 3. Conclusion.

Hence, the third term of the expansion is $T_{3} = 28 x^{6} y^{2}$ .

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