TUTORIALS:

FOIL Multiplying Polynomials
Examples
What to Do 
How to Do It 
1. Recall the Foil Method to multiply (x + 2)(2x + 3) =
F = the product of the first terms: xÂ·2x = 2x^{2}
O = the product of the outer terms xÂ·3 = 3x
Ι = the product of the inner terms 2Â·2x = 4x
L = the product of the last terms 2Â·3 = 6
Algebraically add the O + Ι = 3x + 4x = 7x.
Drawing the â€œframesâ€ help organize the steps
in the beginning as you are learning. 
→ (x + 2)(2x + 3)
2x^{2} + 7x + 6 
2. For
general linear (first degree) binomials with common terms:
Find the product of the firsts , the algebraic sum
of the outer and inner and the product of the
lastsâ€. Then add all algebraically.
Algebraically add the O + Ι = 28x 0 3x = 25x.
The algebraic sum is the Product: 
→ (x + 7)(4x  3)

3. For general linear (first degree) binomials
with common terms:
Find the product of the firsts , the algebraic sum
of the outer and inner and the product of the
lastsâ€.
Then add all algebraically.
Algebraically add the O + Ι = 16x 0 9x =  25x.
The algebraic sum is the Product:

→ (3x  4)(4x  3)
12x^{2}  25x + 12 
4.
For general linear (first degree) binomials with â€œlike termsâ€:
Find the product of the firsts, the algebraic sum
of the outer and inner and the product of the
lastsâ€.
Then add all algebraically.
Algebraically add the O + Ι = + 6x  6x = 0 .
The algebraic sum is the Product:

→ (2x + 3) (2x  3)
= 4x^{2}  9 
5. For general linear (first degree) binomials
with â€œlike termsâ€:
Find the product of the firsts , the algebraic sum
of the outer and inner and the product of the
lastsâ€.
Then add all algebraically.
Algebraically add the O + Ι = + 15x 15x = 0 .
The algebraic sum is the Product:

→ (3x + 5) (3x  5)
= 9x^{2}  25 
