FOIL
And Exponents
©M. Pickens 2006
Objectives
• To learn the multiplication exponent rule
• To review the distributive property
• To learn how to FOIL.
• To learn about the box method
©M. Pickens 2006
Exponents
• What does 72 mean? 7 ● 7
• What does 32 mean?
3●3
• What does (-2)2 mean? (-2) ● (-2)
• What does x2 mean?
x●x
©M. Pickens 2006
Don’t get these confused
©M. Pickens 2006
Exponents
• What does 73 mean? 7 ● 7 ● 7
• What does 35 mean?
3●3●3●3●3
• What does (-2)6 mean? (-2)(-2)(-2)(-2)(-2)(-2)
• What does x9 mean?
x●x●x●x●x●x●x●x●x
©M. Pickens 2006
More Exponents
If there is no exponent
showing it is 1
x  x  x  ( x  x)  x
2
1
3
y  y  ( y  y  y  y  y)  ( y  y)  y 7
5
2
p  p ( p  p  p)  ( p  p  p  p  p)  p8
3
5
Notice: When multiplying with the same
variable you can add the exponents
©M. Pickens 2006
More Practice
y y  y
9
4
r r  r
13
(2)( 2h)  4h
7
1
4
6
3
4
9
7
(7 g )(10 f )(3 f )  210 g f
5
8
(5 g )(2 g ) 10g
3
(4k )(2k )(5k )  40k
2
1
5
7
©M. Pickens 2006
Distributive Property
-7(5x + 8) = -7(5x)+ -7(8) = -35x – 56
x(x + 4)
= x(x) + x(4)
= x2 + 4x
2x(x – 6) = 2x(x) + 2x(-6) = 2x2 – 12x
©M. Pickens 2006
Distributive Property
3h2(5h – 9) = 3h2(5h)+ 3h2(-9) = 15h3 – 27h2
9p3(2p5 + 6p) = 9p3(2p5) + 9p3(6p) = 18p8 + 54p4
7k(k9 – 6k) = 7k(k9) + 7k(-6k) = 7k10 – 42k2
©M. Pickens 2006
What is FOIL
• Foil is an
acronym to
help when
multiplying
two
binomials
• It stands for
©M. Pickens 2006
FOIL Examples
First Outer Inner Last
(x + 3)(3x + 9) =x(3x) +x(9) +3(3x) + 3(9)
=3x2 + 9x + 9x + 27
=3x2 + 18x + 27
(-2x – 4 )(x – 6 )=-2x(x) +-2x(-6) +-4(x)+ -4(-6)
=-2x2 + 12x + -4x + 24
=-2x2 + 8x + 24
©M. Pickens 2006
FOIL Examples
First Outer Inner Last
(x – 9)(x + 9) =x(x) +x(9) +-9(x) + -9(9)
=x2 + 9x + -9x + -81
= x2 – 81
(4x + 2 )(x – 8) =4x(x) +4x(-8) +2(x) + 2(-8)
=4x2 +-32x + 2x + -16
= 4x2 – 30x – 16
©M. Pickens 2006
FOIL Examples
First Outer Inner Last
Try these on your own
(7x – 2)(3x + 5) =7x(3x) +7x(5)+-2(3x)+ -2(5)
=21x2 + 35x + -6x + -10
= 21x2 – 29x – 10
(x – 2)(x + 2)
=x(x) +x(2) +-2(x) + -2(2)
= x2 + 2x + -2x + -4
= x2 – 4
©M. Pickens 2006
FOIL Examples
First Outer Inner Last
(3x – 2y)(x + y) =3x(x) +3x(y)+-2y(x) + -2y(y)
=3x2 + 3xy + -2xy + -2y2
= 3x2 + xy – 2y2
(5x – 2)(3 – y ) =5x(3)+5x(-y)+-2(3) + -2(-y)
= 15x + -5xy + -6 + 2y
©M. Pickens 2006
FOIL Examples
First Outer Inner Last
Try these on your own
(3 – x)(2y + 5) =3(2y) +3(5) +-x(2y)+ -x(5)
=6y + 15 + -2xy + -5x
(-2x – 2y)(3y + 4x)=-2x(3y)+-2x(4x)+-2y(3y)+-2y(4x)
= -6xy + -8x2 + -6y2 + -8xy
= -14xy – 8x2 – 6y2
©M. Pickens 2006
FOIL Examples
First Outer Inner Last
(x – 3)2 =(x – 3)(x – 3)
=(x – 3)(x – 3) =x(x) +x(-3) + -3(x) + -3(-3)
=x2 + -3x + -3x + 9
=x2 – 6x + 9
©M. Pickens 2006