What to Do 
How to Do It 
1. The most basic property of algebra
necessary to multiplying polynomials is the distributive property. 
→
A(B + C) = AB + AC 
2. This can be extended to several terms inside
the parenthesis: (The three dots ... mean
and so on in the pattern.) 
→
A(B + C + D + ... )
= AB + AC + AD + ... 
3. Both multiplicands may be binomials, in which
case the property is usually referred to as the
â€œdouble distributive propertyâ€. 
→ (A + B)(C + D)
= A(C + D) + B(C + D)
= AC + AD + BC + BD 
4. Consider the following examples: 

a) 2(x + 3) = 
→
2(x + 3)
= 2x + 2Â·3
= 2x + 6 
b) 3x(x1) = 
→
3x(x  1)
= 3xÂ·x + 3xÂ·(1)
= 3x^{2}  3x 
c)  5(x2 + 2x  3) = 
→ 
5(x^{2} + 2x  3)
= ( 5)(x^{2}) + ( 5)(2x) + ( 5)( 3)
=  5x^{2}  10x + 15 
d) (x + a)(y + b) = 
→ (x + a)(y + b)
= x(y + b) + a(y + b)
= xy + xb + ay + ab 
e) (x + 2)(2x + 3) = With practice we can do the second
line in our head and go directly to the
third line. 
→
(x + 2) (2x + 3)
= x (2x + 3) + 2(2x + 3)
= xÂ·2x + xÂ·3
+ 2Â·2x + 2Â·3
= 2x^{2} + 3x + 4x + 6
= 2x^{2} + 7x + 6

f) (2x + 3)(2x + 3) =
Later, skip this second line and →
go directly to this third line. → 
→
(2x + 3) (2x + 3)
= 2xÂ·2x + 2xÂ·3
+ 3Â·2x + 3Â·3
= 4x^{2} + 6x + 6x + 9
= 4x^{2} + 12x + 9 
g) (2x + 3)(2x  3) =
Note the â€œequal and oppositesâ€ →
cancel out here. 
→ (2x + 3) (2x
 3)
= 2xÂ·2x + 2xÂ·(
3) + 3Â·2x + 3Â·(
3)
= 4x^{2}  6x + 6x  9
= 4x^{2}  9 