FOIL PATTERN In using the distributive property for multiplying two binomials,
you may have noticed the following pattern. Multiply the First, Outer, Inner, and
Last terms. Then combine like terms. This pattern is called the FOIL pattern.
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Product of
First terms
Product of
Outer terms
Product of
Inner terms
Product of
Last terms
(3x 4)(x 5) 3x2 15x 4x 20
3x2 19x 20
2
EXAMPLE
Combine like terms.
Multiply Binomials Using the FOIL Pattern
F
O
I
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(2x 3)(2x 1) 4x2 2x 6x 3
4x2 8x 3
Combine like terms.
Multiply Binomials Using the FOIL Pattern
Use the FOIL pattern to find the product.
4. (x 1)(x 4)
5. (2x 3)(x 1)
6. (x 2)(2x 1)
To multiply two polynomials that have three or more terms, remember that each
term of one polynomial must be multiplied by each term of the other polynomial.
Use a vertical or a horizontal format. Write each polynomial in standard form.
3
EXAMPLE
Multiply Polynomials Vertically
Find the product (x 2)(5 3x x2).
Solution
Line up like terms vertically. Then multiply as shown below.
x2 3x 5
Standard form
x2
Standard form
2x2 6x 10
2(x2 3x 5)
x3 3x2 5x
x (x2 3x 5)
x3 5x2 x 10
Combine like terms.
Multiply Polynomials Vertically
Use a vertical format to find the product.
7. (x 1)(x2 3x 2)
576
Chapter 10
Polynomials and Factoring
8. (2x 1)(2x2 x 3) 9. (2x 3)(3x2 x 4)