Mathematics

Grade10

Easy

Question

# What is the value of *n*, if the coefficients of the second term of (x – y)^{3} is equal to the third term of the expansion (x + y)^{n}?

- - 2
3

- 4
- 5

3

## The correct answer is: 3

### STEP BY STEP SOLUTION

Coefficient of the second term of (x – y)^{3} is ^{3}C_{1}, and the coefficient of the third term of the expansion (x + y)^{n} is ^{n}C_{2}.

^{3}C_{1} = ^{n}C_{2}

3 = n!÷2!(n–2)!

6 = n(n−1)(n−2)!÷(n–2)!

6 = n^{2} – n

n^{2} – n – 6 = 0

n^{2} – 3n + 2n – 6 = 0

(n – 3) (n + 2) = 0

n = 3, – 2

Since *n* cannot be negative, n = 3.

*n*cannot be negative, n = 3.

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