Question

How many terms are there in the expansion of (x+a)^n-1​

Answer 1

Hey..

Concept:

In the binomial expansion of (a + b) n, there are total n + 1 terms.

Calculation:

⇒ (1 + 2x + x2) 5 + (1 + 4y + 4y2) 5 = (1 + x) 2 × 5 + (1 + 2y)2 × 5

= (1 + x) 10 + (1 + 2y)10

As we know that, in the binomial expansion of (a + b) n, there are total n + 1 terms.

⇒ The no. of terms in the binomial expansion of (1 + x) 10 and (1 + 2y)10 is 11

∴ The no. of terms in the binomial expansion of (1 + x) 10 + (1 + 2y)10 = 11 + 11 - 1 = 21

Answer 2

Hey..

Concept:

In the binomial expansion of (a + b) n, there are total n + 1 terms.

Calculation:

⇒ (1 + 2x + x2) 5 + (1 + 4y + 4y2) 5 = (1 + x) 2 × 5 + (1 + 2y)2 × 5

= (1 + x) 10 + (1 + 2y)10

As we know that, in the binomial expansion of (a + b) n, there are total n + 1 terms.

⇒ The no. of terms in the binomial expansion of (1 + x) 10 and (1 + 2y)10 is 11

∴ The no. of terms in the binomial expansion of (1 + x) 10 + (1 + 2y)10 = 11 + 11 - 1 = 21