MULTIPLYING BINOMIALS USING FOIL METHOD

Two binomials can be multiplied using the FOIL method.

F - First terms

O - Outer terms

I - Inner terms

L - Last terms

Example 1 :

Multiply.

(3x + 2)(x + 3) 

Solution :

Step 1 :


F



O



I



L


Step 2 :

Combining the terms.

  =  3x2 + 9x + 2x + 6

  =  3x2 + 11x + 6

Example 2 :

Multiply.

(x - 1)(2x - 2) 

Solution :

Step 1 :

F

x (2x)  =  2x(1+1)  =  2x2

O

x (-2)  =  -2x

I

-1 (2x)  =  -2x

L

-1 (-2)  =  2

Step 2 :

Combining the terms.

  =  2x2 - 2x - 2x + 2

  =  2x2 - 4x + 2

Example 3 :

Multiply.

(2x + 3)(2x - 3) 

Solution :

Step 1 :

F

2x (2x)  =  4x(1+1)  =  4x2

O

2x (-3)  =  -6x

I

3 (2x)  =  6x

L

+3 (-3)  =  -9

Step 2 :

Combining the terms.

  =  4x2 - 6x + 6x - 9

  =  4x2 - 9

Example 4 :

Multiply.

(x + 1)(x - 3)

Solution :

Step 1 :

F

x (x)  =  x(1+1)  =  x2

O

x (-3)  =  -3x

I

1 (x)  =  x

L

+1 (-3)  =  -3

Step 2 :

Combining the terms.

  =  x2 - 3x + x - 3

  =  x2 - 2x - 3

Example 5 :

Multiply.

(4x + 1)(5x - 8)

Solution :

Step 1 :

F

4x (5x)  =  20x(1+1)  =  20x2

O

4x (-8)  =  -32x

I

1 (5x)  =  5x

L

+1 (-8)  =  -8

Step 2 :

Combining the terms.

  =  20x2 - 32x + 5x - 8

  =  20x2 - 27x - 8

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