Multiplying Binomials

PROBLEM #1

(4x - 4)(x + 4)

FOIL
First
Outside
Inside
Last

Step One
First:
• The first term in the first binomial is 4x
• The first term in the second binomial is x
• So we multiply them: (4x)(x) = 4x2

Step Two
Outside:
• The outside term in the first binomial is 4x
• The outside term in the second binomial is 4
• So we multiply them: (4x)(4) = 16x

Step Three
Inside:
• The inside term in the first binomial is - 4
• The inside term in the second binomial is x
• So we multiply them: (- 4)(x) = - 4x

Step Four
Last:
• The last term in the first binomial is - 4
• The last term in the second binomial is 4
• So we multiply them: (- 4)(4) = - 16

Step Five
• Write out your calculations as one equation:
• 4x2 + 16x – 4x – 16

Step Six
• Combine like terms
• The 16x and - 4x are the only set of terms that are like
• 16x – 4x = 12x
• Therefore your answer is:

ANSWER
4x2 + 12x – 16



PROBLEM #2

(4x - 4)(3x + 2)

FOIL
First
Outside
Inside
Last

Step One
First:
• The first term in the first binomial is 4x
• The first term in the second binomial is x
• So we multiply them: (4x)(3x) = 12x2

Step Two
Outside:
• The outside term in the first binomial is 4x
• The outside term in the second binomial is 4
• So we multiply them: (4x)(2) = 8x

Step Three
Inside:
• The inside term in the first binomial is - 4
• The inside term in the second binomial is x
• So we multiply them: (- 4)(3x) = - 12x

Step Four
Last:
• The last term in the first binomial is - 4
• The last term in the second binomial is 4
• So we multiply them: (- 4)(2) = - 8

Step Five
• Write out your calculations as one equation:
• 12x2 + 8x – 12x – 8

Step Six
• Combine like terms
• The 8x and - 12x are the only set of terms that are like
• 8x – 12x = - 4x
• Therefore your answer is:

ANSWER
12x2 - 4x – 8