Question

The total number of terms in the expansion of (x + a)¹⁰⁰ + (x – a)¹⁰⁰ after simplification is ______.

Options

• 50

• 202

• 51

• None of these

Answer 1

The total number of terms in the expansion of (x + a)¹⁰⁰ + (x – a)¹⁰⁰ after simplification is 51.

Explanation:

Number of terms in the expansion of (x + a)¹⁰⁰ = 101

Number of terms in the expansion of (x – a)¹⁰⁰ = 101

Now 50 terms of expansion will cancel out with negative 50 terms of (x – a)¹⁰⁰ 

So, the remaining 51 terms of first expansion will be added to 51 terms of other

Therefore, the number of terms = 51