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 Number of inequalities to solve: 23456789
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# Multiplying Binomials Using the FOIL Method

FOIL can be used to multiply any two binomials. The binomials in the next example have powers higher than 1.

Example 1

Using the FOIL method

Find each product.

a) (x3 - 3)(x3 + 6)

b) (2a2 + 1)(a2 + 5)

Solution

 a) (x3 - 3)(x3 + 6) = x6 + 6x3 - 3x3 - 18 = x6 + 3x3 - 18
 b) (2a2 + 1)(a2 + 5) = 2a4 + 10a2 + a2 + 5 = 2a4 + 1a2 + 5

## Multiplying Binomials Quickly

The outer and inner products in the FOIL method are often like terms, and we can combine them without writing them doun. Once you become proficient at using FOIL, you can find the product of two binomials without writing anything except the answer.

Example 2

Using FOIL to find a product quickly

Find each product. Write down only the answer.

a) (x + 3)(x + 4)

b) (2x - 1)(x + 5)

c) (a - 6)(a + 6)

Solution

 a) (x + 3)(x + 4) = x2 + 7x + 12 Combine like terms: 3x + 4x = 7x. b) (2x - 1)(x + 5) = 2x2 + 9x - 5 Combine like terms:10x - x = 9x. c) (a - 6)(a + 6) = a2 - 36 Combine like terms: 6a - 6a = 0