Multiplying two binomials: distributive property

There are many different quick and efficient ways to multiply two binomials. One of them being distributive property.

Examples

(x-6)(x+12)

Step 1: Multiply the x in the first bracket with the x in the second bracket.

Step 2: Multiply the x with the 12.

Step 3: Multiply the -6 with the x in the second bracket.

Step 4: Multiply the -6 with 12.

Step 5: Write the products of the numbers in a line. This is the expanded form.

Step 6: Simplify. Add the like numbers together.

Multiplying two Binomials: Area Model

Using an area model to multiply two binomials is an easy and a great visual way to do so.

(2x+3)(x+12)

Step 1: Create a rectangular diagram and write out the monomials, one on top and one on the side.

Step 2: In the first box you put the product of x multiplied by 2x.

Step 3: In the second box you put the product of x multiplied by 3.

Step 4: Do the same with the bottom two boxes. The bottom left box is the product of 12 and 2x, the right box is the product of 12 and 3.

Step 5: Write the numbers in the boxes in a line. This is expanded form.

 

Step 6: Simplify.

a binomial is a polynomial that is the sum of two terms,

Why?

It is important to know the different ways in making multiplying binomials easy and quick. It will help in polynomial related math problems in the future and make it much easier for you to do the steps in solving the problems.

Vocabulary

Binomial- A polynomial that consists of two terms.