| 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: x·2x = 2x2
O = the product of the outer terms x·3 = 3x
Ι = the product of the inner terms 2·2x = 4x
L = the product of the last terms 2·3 = 6
Algebraically add the O + Ι = 3x + 4x = 7x.
Drawing the “frames†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 “like 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 “like 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 |