distributive property of multiplication and the foil method
TRANSCRIPT
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Multiplying BinomialsDistributive Property of Multiplication and
the FOIL Method
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Primary Objective: To find the product of two binomials
Secondary Objective: To review the Distributive Property of Multiplication and to learn the FOIL Method.
Objectives
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a(b+c) = a(b+c) = ab + acor
(b+c)a = (b+c)a = ba + ca
What property tell us that both results are the same (i.e. that ab + ac = ba + ca)?
The Commutative Property
Distributive Property of Multiplication (with respect to addition)
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a(b-c) = a(b-c) = ab-acor
(b-c)a = (b-c)a = ba-ca
Again, per the Commutative Property, ab-ac = ba-ca
Distributive Property of Multiplication (with respect to subtraction)
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(a+b)(c+d)
First distribute the multiplication of a to c and d , then distribute the multiplication of b to
c and d.
(a+b)(c+d) = ac + ad + bc + bd
The Distributive Property Works for Two Binomials
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(a+b) (c+d) =
ac + ad + bc + bd First Outer Inner Last Terms Terms Terms Terms
This is called the FOIL Method
FOIL Method
Outer
Inner
First
Last
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Learn the FOIL Methodbut remember that you are
using the
DISTRIBUTIVE PROPERTY
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Example 1: Distributive Property of Multiplication (with respect to addition)
(2x+5)(3x+4)
(2x+5)(3x+4)
6x2 + 8x + 15x + 20 = First Outer Inner Last
combine like terms6x2 + 23x + 20
OuterInner
First Last
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Example 2: Distributive Property of Multiplication (with respect to subtraction)
(3h+5)(3h-1)
(3h+5) (3h-1)
9h2 - 3h + 15h - 5 = First Outer Inner Last
combine like terms9h2 + 12h - 5
OuterInner
First Last
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Your turn (with addition):
(n+7)(2n+5)
(n+7)(2n+5) =
2n2 + 5n + 14n + 35 =
2n2 + 19n + 35
Outer
Inner
First
Last
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Your turn (with subtraction):
(z+4)(z-7)
(z+4) (z-7) =
z2 – 7z + 4z - 28 =
z2 - 3z – 28
Hint: draw line through “z” so you don’t confuse with “2”
Outer
Inner
First
Last