Double Distributive Method for Multiplying Binomials

Like Foil, the double distributive method is used for multiplying 2 binomials.

How "double" distributive works

Unlike "single" distribution which only distributes 1 single term , double distribution requires two terms (a binomial) to distribute over a second binomial .

So, in this example, you have to distribute that first x and also that 5 over the second binomial .

Double vs  Single Distributive Property
Problem 1

Use double distributive method to simplify $$ (x -3)(x+7) $$

Step 1

Distribute out both terms

double distributive problem 1
Step 2

Simplify like terms

$ -3x -21 + x^2 + 7x \\ x^2 + 4x - 21 $
Problem 2

Use double distributive method to simplify $$ (x -3)(x+3) $$

Step 1

Distribute out both terms

double distributive problem 1
Step 2

Simplify like terms

$ -3x -9 + x^2 + 3x \\ x^2 \red{-3x + 3x} -9 \\ x^2 -9 $
Problem 3

Use double distributive method to simplify $$ (x - 2)(2x+6) $$

Step 1

Distribute out both terms

double distributive problem 1
Step 2

Simplify like terms

$ -4x -12 + 2x^2 + 6x \\ 2x^2 +2x - 12 $
Problem 4

Use double distributive method to simplify $$ (x -8)(3x - 1 ) $$

Step 1

Distribute out both terms

double distributive problem 5
Step 2

Simplify like terms

$ -24x +8 + 3x^2 -x \\ x^2 -25x +8 $

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