Chapter 12: Q. 12.75. (page 1211)

Find the third term of ${(x + y)}^{6}$

Short Answer

Expert verified

The third of the expansion is $15 x^{4} y^{2}$

Step by step solution

Step 1. Use the r+1st term formula.

The ${(r + 1)}^{s t}$ term in the binomial expansion of ${(a + b)}^{n}$ is $(\begin{matrix} n \\ r \end{matrix}) a^{n - r} b^{r}$

Substitute in the values into the binomial expansion,

$a = x b = y n = 6$

Step 2. Substitute the values into the formula and simplify.

We are looking for the third term.

since $r + 1 = 3$

then $r = 2$ .

Simply the expression,

${(x + y)}^{6} = (\begin{matrix} 6 \\ 2 \end{matrix}) x^{6 - 2} y^{2} = \frac{6!}{2! 4!} x^{4} y^{2} = 15 x^{4} y^{2}$

Step 3. Conclusion.

Therefore, the third term of the given expression is $15 x^{4} y^{2}$

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Find the third term of ${(x + y)}^{6}$

Short Answer

Step by step solution

Step 1. Use the r+1st term formula.

Step 2. Substitute the values into the formula and simplify.

Step 3. Conclusion.

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Find the third term ofx+y6

Short Answer

Step by step solution

Step 1. Use the r+1st term formula.

Step 2. Substitute the values into the formula and simplify.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Find the third term of ${(x + y)}^{6}$