1. Multiplying Binomials

2. Binomial An algebraic expression which contains two terms
is known as Binomial 
Example 1 : 2x + 3x2 
It is a Binomial, because it contains two terms 2x and 3x2 
Example 2 : 9pq + 11p2q
It is a Binomial, because it contains two terms 9pq and 11p2q

3. "FOIL" Method  for multiplying binomial
FOIL stands for "First, Outer, Inner, Last" 
It is the sum of:
· multiplying the First terms of each binomial,
· multiplying the Outer terms of each binomial,
· multiplying the Inner terms of each binomial, and
· multiplying the Last terms of each binomial
Recap: Multiplying powers with the same base:
Add the exponents. (am)x(an) = am+n
For example: ( a3 )x(a2) = a3+2 = a5

4. Ans: 2y2+ 9y + 10 Example 1: (2y + 5)(y + 2) Solution:
F: (2y + 5) (y + 2)
O: (2y + 5) (y + 2)
I: (2y + 5) (y + 2)
L: (2y+ 5) (y + 2)
F : Multiplying the first term of each binomial we get (2y) x y = 2y2
O : Multiplying the outer term of each binomial, we get (2y) x (2) = 4y
I : Multiplying the inner term of each binomial, we get 5 x y = 5y
L : Multiplying the last term of each binomial, we get 5 x 2= 10
After taking sum of above , we get 2y2 + 4y + 5y + 10
= 2y2+ 9y + 10
Ans: 2y2+ 9y + 10

5. Ans: 6x2 + 7x - 3 Example 2: (2x + 3)(3x – 1) F : (2x + 3) (3x - 1)
Solution:
F : (2x + 3) (3x - 1)
O : (2x + 3) (3x - 1)
I : (2x + 3) (3x - 1)
L : (2x + 3) (3x - 1)
F : Multiplying the first term of each binomial we get 2x x 3x = 6x2
O : Multiplying the outer term of each binomial, we get 2x x (-1) = -2x
I : Multiplying the inner term of each binomial, we get 3 x 3x = 9x
L : Multiplying the last term of each binomial, we get 3 x (-1) = -3
After taking sum of above , we get 6x2 +(-2x) + 9x + (-3)
= 6x2 - 2x + 9x - 3
= 6x2 + 7x - 3
Ans: 6x2 + 7x - 3

6. Try These
Multiply (2j + 6) (j + 4)
Multiply (3m + 8) (2m - 9)