x plus a into x plus b

In this section, you will learn the formula or expansion for (x + a)(x + b).

That is, 

(x + a)(x + b)  =  x2 + xb + xa + ab

(x + a)(x + b)  =  x2 + (b + a)x + ab

(x + a)(x + b)  =  x2 + (a + b)x + ab

Solved Problems

Problem 1 :

Find the product of : 

(x + 2)(x + 3)

Solution : 

(x + 2)(x + 3) is in the form of (x + a)(x + b)

Comparing (x + a)(x + b) and (x + 2)(x + 3), we get

x  =  x

a  =  2

b  =  3

Write the formula / expansion for (x + a)(x + b).

(x + a)(x + b)  =  x2 + (a + b)x + ab

Substitute x for x, 2 for a and 3 for b. 

(x + 2)(x + 3)  =  x2 + (2 + 3)x + (2)(3)

(x + 2)(x + 3)  =  x2 + 5x + 6

So, the product of (x + 2) and (x + 3) is  

x2 + 5x + 6

Problem 2 :

Find the product of : 

(2p + 1)(2p + 3)

Solution : 

(2p + 1)(2p + 3) is in the form of (x + a)(x + b)

Comparing (x + a)(x + b) and (2p + 1)(2p + 3), we get

x  =  2p

a  =  1

b  =  3

Write the formula / expansion for (x + a)(x + b).

(x + a)(x + b)  =  x2 + (a + b)x + ab

Substitute 2p for x, 1 for a and 2 for b. 

(2p + 1)(2p + 3)  =  (2p)2 + (1 + 3)(2p) + (1)(3)

(2p + 1)(2p + 3)  =  4p2 + (4)(2p) + 3

(2p + 1)(2p + 3)  =  4p2 + 8p + 3

So, the product of (2p + 1) and (2p + 3) is  

4p2 + 8p + 3

plus a times x minus b - Formula

(x + a)(x - b)  =  x2 - xb + xa - ab

(x + a)(x - b)  =  x2 + xa - xb - ab

(x + a)(x - b)  =  x2 + (a - b)x - ab

x minus a times x plus b - Formula

(x - a)(x + b)  =  x2 + xb - xa - ab

(x - a)(x + b)  =  x2 - xa + xb - ab

(x - a)(x + b)  =  x2 - (a - b)x - ab

x minus a times x minus b - Formula

(x - a)(x - b)  =  x2 - xb - xa + ab

(x - a)(x - b)  =  x2 - xa - xb + ab

(x - a)(x - b)  =  x2 - (a + b)x + ab

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