Question

Use the binomial Theorem to write the 5th term of the binomial expression

1.) (2y-5)^9 2.) (x+3y^2)^11

Answer 1

1. 2,520,000 y^5.

2. 26730 x^7 y^8.

Explanation:

1. (2y - 5)^9

(r + 1)th term of (a + b)^n = nCr a^(n-r) b^r

So the 5th, (4+1)th term, = 9C4 (2y)^(9-4) (-5)^4

= 126 * 2^5 * y^5 * 625

= 2,520,000 y^5.

2. ( x + 3y^2)^11.

5th term = 11C4 x^(11-4) (3y^2)^4

= 330*x^7*81*y^8.

= 26730 x^7 y^8.