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# More on the Distribution Property—the FOIL Method Help

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By McGraw-Hill Professional
Updated on Sep 26, 2011

## The Distributive Property Using FOIL

The FOIL method helps us to use the distribution property to help expand expressions like ( x + 4)(2 x − 1). The letters in “FOIL” describe the sums and products.

#### Examples

( x + 16)( x – 4) = x · x + x (–4)+ 16 x + 16(–4) = x 2 – 4 x + 16 x – 64

= x 2 + 12 x – 64

(2 x + 3)(7 x – 6) = 2 x (7 x )+ 2 x (–6)+ 3(7 x )+ 3(–6)

= 14 x 2 – 12 x + 21 x – 18 = 14 x 2 + 9 x – 18

(2 x + 1) 2 = (2 x + 1)(2 x + 1) = 2 x (2 x ) + 2 x (1) + 1(2 x ) + 1(1)

= 4 x 2 + 2 x + 2 x + 1 = 4 x 2 + 4 x + 1

( x – 7)( x + 7) = x · x + 7 x +(–7) x +(–7)(7) = x 2 + 7 x – 7 x − 49

= x 2 – 49

## The Distributive Property Using FOIL Practice Problems

#### Practice

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 2y)(x + 2 y) =

8. (x – 5)(x + 5) =

9. (x – 6)(x + 6) =

11. ( x + 8) 2 =

12. (xy) 2 =

13. (2x + 3y) 2 =

#### Solutions

1. (5x – 1)(2x + 3) = 5x (2x) + 5x (3)+(–1)(2x)+(–1)(3)

= 10x 2 + 15x – 2x – 3 = 10x 2 + 13x – 3

2. (4x + 2)(x – 6) = 4x ( x ) + 4x(–6) + 2x + 2(–6)

= 4x 2 – 24 x + 2 x – 12 = 4 x 2 – 22 x – 12

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

= 18x 2 + 8x + 9x + 4 = 18x 2 + 17x + 4

4. (12x – 1)(2x – 5) = 12x (2x )+ 12x (–5)+(–1)(2x )+(–1)(–5)

= 24x 2 – 60 x – 2 x + 5 = 24 x 2 – 62 x + 5

5. (x 2 + 2)(x – 1) = x 2 ( x )+ x 2 (–1)+ 2x + 2(–1) = x 3x 2 + 2x – 2

6. (x 2y)(x + 2y) = x 2 (x)+ x 2 (2y)+(– y) x +(– y)(2 y)

= x 3 + 2 x 2 yxy – 2 y 2

8. ( x – 5)( x + 5) = x ( x )+ 5 x +(–5) x +(–5)(5)

= x 2 + 5 x – 5 x – 25 = x 2 – 25

9. (x – 6)(x + 6) = x (x )+ 6x +(–6) x +(–6)(6)

= x 2 + 6 x – 6 x – 36 = x 2 – 36

11. (x + 8) 2 = (x + 8)(x + 8) = x (x) + 8x + 8x + 8(8)

= x 2 + 16 x + 64

12. ( xy) 2 = ( xy)( xy) = x ( x)+ x (– y)+ x (– y)+(– y)(– y)

= x 2xyxy + y 2 = x 2 – 2xy + y 2

13. (2 x + 3 y) 2 = (2 x + 3y)(2x + 3y)

= 2x (2x)+ 2x (3y)+ 3y (2x)+(3y)(3y)

= 4x 2 + 6xy + 6xy + 9y 2 = 4x 2 + 12xy + 9y 2

Practice problems for this concept can be found at: Algebra Factoring Practice Test.

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