Multiplying Two Brackets (Binomial Expressions)

A binomial expression contains two terms:  

\( \scriptsize \underset{(1st\: term)}{2x} \: + \: \underset{(2nd\: term)}{3y} \: \normalsize \rightarrow \: \scriptsize Binomial \: Expression \)

In multiplying two binomial expressions like (a + b) and (x + y), follow these steps, 

(a + b)  (x + y) 

Step 1: a (x + y) 

Step 2: +b (x + y) 

Step 3: Join step 1 and 2 → (a + b) (x + y) = a (x + y) + b (x + y) 

∴ (a – b) (x – y) = a(x – y) – b(x – y) 

Example 3.1.1:

Expand and simplify the following: 

a. (4x + 1)(x + 2)
b. (3x + 2)(2x + 3) 
c. (4f – 2) (3f – 3)
d. 10(2 + x) (3 + 2x) 

Solution 

a. (x + 1)(x + 2) = x(x + 2) + 1(x + 2) 

  = x(x) + x(2) + 1(x) + 1(2) 

= x² + 2x + x + 2 

= x² + 3x + 2 

b. (3x + 2) (2x + 3)

= 3x(2x + 3) + 2(2x + 3) 

= 3x (2x) + 3x (3) + 2(2x) + 2(3) 

= 6x² + 9x + 4x + 6 

= 6x² + 13x + 6  

c. (4f – 2) (3f – 3)

= 4f(3f – 3) – 2(3f – 3) 

= 4f(3f) + 4f(-3) – 2(3f) – 2(-3) 

= 12f² – 12f – 6f + 6 

= 12f² – 18f + 6 

d. 10 (2 + x)(3 + 2x)

= 10[2(3 + 2x) + x(3 + 2x)] 

= 10 [2(3) +2(2x) + x(3) + x(2x)]

= 10 [6 + 4x + 3x + 2x²]

= 10 [6 + 7x + 2x²]

= 10(6) + 10(7x) + 10(2x²) 

= 60 + 70x + 20x²

Evaluation Questions: