5.4 Special Products

The FOIL Method When multiplying 2 binomials, the distributive property can be easily remembered as the FOIL method. F – product of First terms O – product of Outside terms I – product of Inside terms L – product of Last terms

Multiply (y – 12)(y + 4). Example

Multiply (2x – 4)(7x + 5). Example

In the process of using the FOIL method on products of certain types of binomials, we see specific patterns that lead to special products. Special Products

Squaring a Binomial A binomial squared is equal to the square of the first term plus or minus twice the product of both terms plus the square of the second term. (a + b) 2 = a 2 + 2ab + b 2 (a – b) 2 = a 2 – 2ab + b 2 Special Products

Example Multiply. (x + 6) 2

Example a. (12a – 3) 2 b. (x + y) 2 Multiply.

Multiplying the Sum and Difference of Two Terms The product of the sum and difference of two terms is the square of the first term minus the square of the second term. (a + b)(a – b) = a 2 – b 2 Special Products

Example Multiply. (2x + 4)(2x – 4)

Example Multiply. a. (5a + 3)(5a – 3) b. (8c + 2d)(8c – 2d)

Example Use a special product to multiply, if possible. a. (7a + 4) 2 b. (c + 0.2d)(c – 0.2d) c.