When you use the Distributive Property to multiply binomials, notice that you multiply each term of the first binomial by each term of the second binomial. A table can help you organize your work.

There is a shortcut you can use to multiply two binomials. Consider the product of 2 x + 2 2 x plus 2  and x + 3 . x plus 3 .  The large rectangle below models this product. You can divide the large rectangle into four smaller rectangles.

The area of the large rectangle is the sum of the areas of the four smaller rectangles.

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( 2 x + 2 ) ( x + 3 ) = ( 2 x ) ( x ) + ( 2 x ) ( 3 ) + ( 2 ) ( x ) + ( 2 ) ( 3 )   = 2 x 2 + 6 x + 2 x + 6   = 2 x 2 + 8 x + 6     ◄ The area of each rectangle is the product of one term of  2 x + 2 and one term of  x + 3. table with 1 row and 3 columns , row1 column 1 , table with 3 rows and 9 columns , row1 column 1 , open 2 x plus 2 close open x plus 3 close , column 2 equals , column 3 open 2 x close open x close , column 4 plus , column 5 open 2 x close open 3 close , column 6 plus , column 7 open 2 close open x close , column 8 plus , column 9 open 2 close open 3 close , row2 column 1 , , column 2 equals , column 3 2 , x squared , column 4 plus , column 5 6 x , column 6 plus , column 7 2 x , column 8 plus , column 9 6 , row3 column 1 , , column 2 equals , column 3 2 , x squared , column 4 plus , column 5 8 x , column 6 plus , column 7 6 , column 8 , column 9 , end table , column 2 black left pointing pointer , column 3 table with 3 rows and 1 column , row1 column 1 , cap theareaofeachrectangleisthe , row2 column 1 , productofonetermof . 2 x plus 2 , row3 column 1 , andonetermof . x plus 3. , end table , end table

This model illustrates another way to find the product of two binomials. You find the sum of the products of the First terms, the Outer terms, the Inner terms, and the Last terms of the binomials. The acronym FOIL may help you remember this method.

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