Page 146 - MarceAlgebra Demystified

CHAPTER 6 Factoring 133

More on the Distribution Property—the FOIL

Method

The FOIL method helps us to use the distribution property to help expand
expressions like ðx þ 4Þð2x 1Þ. The letters in ‘‘FOIL’’ describe the sums and
products.

F F
F First First ðx þ 4Þð2x 1Þ: xð2xÞ¼ 2x 2

O O
þ O Outer Outer ðx þ 4Þð2x 1Þ: xð 1Þ¼ x

II
þ I Inner Inner ðx þ 4Þð2x 1Þ: 4ð2xÞ¼ 8x

L L
þ L Last Last ðx þ 4Þð2x 1Þ: 4ð 1Þ¼ 4

2
2
ðx þ 4Þð2x 1Þ¼ 2x x þ 8x 4 ¼ 2x þ 7x 4

Examples

2
ðx þ 16Þðx 4Þ¼ x x þ xð 4Þþ 16x þ 16ð 4Þ¼ x 4x þ 16x 64
2
¼ x þ 12x 64

ð2x þ 3Þð7x 6Þ¼ 2xð7xÞþ 2xð 6Þþ 3ð7xÞþ 3ð 6Þ
2
2
¼ 14x 12x þ 21x 18 ¼ 14x þ 9x 18
2
ð2x þ 1Þ ¼ð2x þ 1Þð2x þ 1Þ¼ 2xð2xÞþ 2xð1Þþ 1ð2xÞþ 1ð1Þ
2 2
¼ 4x þ 2x þ 2x þ 1 ¼ 4x þ 4x þ 1
2
ðx 7Þðx þ 7Þ¼ x x þ 7x þð 7Þx þð 7Þð7Þ¼ x þ 7x 7x 49
2
¼ x 49