§ 5.4

Special Products

Martin-Gay, Beginning and Intermediate Algebra, 4ed 22

The FOIL Method

When multiplying two binomials, the distributive property can be easily remembered as the FOIL method.

F – product of First termsO – product of Outside termsI – product of Inside termsL – product of Last terms

Martin-Gay, Beginning and Intermediate Algebra, 4ed 33

= y2 – 8y – 48

Multiply (y – 12)(y + 4).

(y – 12)(y + 4)

(y – 12)(y + 4)

(y – 12)(y + 4)

(y – 12)(y + 4)

Product of First terms is y2

Product of Outside terms is 4y

Product of Inside terms is – 12y

Product of Last terms is – 48

(y – 12)(y + 4) = y2 + 4y – 12y – 48F O I L

Using the FOIL Method

Example:

Martin-Gay, Beginning and Intermediate Algebra, 4ed 44

Multiply (2x – 4)(7x + 5).

(2x – 4)(7x + 5) =

= 14x2 + 10x – 28x – 20

F

2x(7x)F

+ 2x(5)O

– 4(7x)I

– 4(5)L

OI

L

= 14x2 – 18x – 20We multiplied these same two binomials together in the previous section, using a different technique, but arrived at the same product.

Using the FOIL Method

Example:

Martin-Gay, Beginning and Intermediate Algebra, 4ed 55

Squaring a Binomial

Squaring a BinomialA 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 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

Example: Multiply (12a 3)2.

(12a 3)2

= 144a2 72a + 9= (12a)2 2(12a)(3) + (3)2

Martin-Gay, Beginning and Intermediate Algebra, 4ed 66

Sum and Difference of Two Terms

Multiplying the Sum and Difference of Two TermsThe 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) = a2 – b2

Example: Multiply (5a + 3)(5a 3).

(5a + 3)(5a 3)= 25a2 9= (5a)2 32

Martin-Gay, Beginning and Intermediate Algebra, 4ed 77

Although you will arrive at the same results for the special products by using the techniques of this section or last section, memorizing these products can save you some time in multiplying polynomials.

Special Products