Algebra Demystified 2nd Ed

152 algebra De mystif ieD

F(first × first) + O(outer × outer) + I(inner × inner) + L(last × last)

FFirst First

FF

×+()xx 42 ()−= 12 :(xx) 2 x^2

+×OOuter Outer +−−=−

OO

()xx 42 () 11 :(xx)

+×IInnerInner +− =

II

()xx 42 () 14 :( 28 xx)

+×LLastLast +−−=−

LL

()xx 42 () 14 :( 14 )

(x + 4)(2x – 1) = 2x^2 – x + 8x – 4 = 2x^2 + 7x – 4

EXAMPLES

Use the FOIL method to expand the product.

(x + 16)(x – 4) = xx⋅⋅xx−

FOIL

+  –+ +

    

 ( 41 )  61  ( 64 ) = x

(^2) – 4x + 16x – 64
= x^2 + 12x − 64
(2x + 3)(7x – 6) = 2x(7x) + 2x(−6) + 3(7x) + 3(−6) = 14x^2 – 12x + 21x – 18
= 14x^2 + 9x – 18
(2x + 1)^2 = (2x + 1)(2x + 1) = 2x(2x) + 2x(1) + 1(2x) + 1(1)
= 4x^2 + 2x + 2x + 1 = 4x^2 + 4x + 1
(x – 7)(x + 7) = x ⋅ x + 7 x + (−7)x + (−7)( 7) = x^2 + 7x – 7x – 49 = x^2 – 49
PRACTICE
Use the FOIL method to expand the product.

1. (5x − 1)(2x + 3) =


2. (4x + 2)(x − 6) =


3. (2x + 1)(9x + 4) =


4. (12x − 1)(2x − 5) =


5. (x^2 + 2)(x − 1) =


6. (x^2 − y)(x + 2y) =

EXAMPLES

Use the FOIL method to expand the product.

PRACTICE

Use the FOIL method to expand the product.