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# Using the â€œFOILâ€ Method to Multiply Two Binomials

To multiply a binomial by a binomial, we use the Distributive Property twice.

For example, letâ€™s multiply (a + b)(c + d).

 Distribute (c + d) to both a and b. (a + b)(c + d) = a(c + d) + b(c + d) Distribute both a and b to  each term in (c + d). = ac + ad + bc + bd

Notice that each term in (a + b) has been multiplied by each term in (c + d).

To remember how to multiply two binomials, we use the word FOIL.

FOIL stands for First, Outer, Inner, Last.

â€¢ The product of the First terms is ac.

â€¢ The product of the Outer terms is ad.

â€¢ The product of the Inner terms is bc.

â€¢ The product of the Last terms is bd. Note:

This picture may help you remember how to use the FOIL method. The arcs form a â€œface.â€ Example 1

Find: (x - 2)(x + 5)

 Solution F O I L Use FOIL.Simplify each product. Combine like terms. (x - 2)(x + 5) == = (x)(x)x2 x2 ++ + (x)(5)5x +- 3x (-2)(x)2x +- - (-2)(5)10 10

So, (x - 2)(x + 5) = x2 + 3x - 10.

Example 2

Find: (3w - 7)(9w - 5)

 Solution F O I L Use FOIL.Simplify each product.Combine like terms. (3w - 7)(9w - 5) == = (3w)(9w)27w2 27w2 +- - (3w)(-5)15w +- 78w (-7)(9w)63w ++ + (-7)(-5)35 35

So, (3w - 7)(9w - 5) = 27w2 - 78w + 35.