# 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 = 2x2 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)  2x2 + 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) 12x2 - 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)  = 4x2 - 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)  = 9x2 - 25