First row
Multiply first row by y
Multiply first row by 2x
Add the columns
)
4
2
y)(4x

(2x
Multiply
2
2
y
xy
3
2
3
2
2
3
3
2
2
2
2
4
10
8
8
4
8
4
2
4
2
4
2
4
y
xy
x
xy
y
x
x
y
xy
y
x
y
x
y
xy
x
Multiply and simplify.
6t + 15
8x
2
+ 13x – 6
4z
3
– 15z
2
+ 13z – 3
5.2 Multiplication of Polynomials
)
1
3
)(
3
4
(
)
2
)(
3
8
(
)
5
2
(
3
2
z
z
z
x
x
t
Real – World Connection:
Business application
5.2 Multiplication of Polynomials
Let the demand, D, or number of games sold in thousands, be given by
, where p ≥ 16 is the price of the games in dollars.
a)
Find the demand where p = $30 and when p = $60.
b)
Write an expression for the revenue, R. Multiply the expression.
c)
Find the revenue when p = $40.
p
D
8
1
40
$1400,000
or
1400
200
1600
)
40
(
8
1
)
40
(
40
$40
p
when
Revenue
c)
8
1
40
)
8
1
40
(
mand)
(price)(de
Revenue
b)
games
500
,
32
)
60
(
8
1
40
$60,
p
when
games
250
,
36
)
30
(
8
1
40
$30,
p
when
a)
2
2
p
p
p
p
D
D
Use the formula
(a + b)
2
=
a
2
+
2ab
+
b
2
(2x + 1)
2
=
(2x + 1)(2x + 1)
where
a
= 2x
and
b
= 1
, then
(2x +1)
2
=
(2x)
2
+
2(2x)(1)
+
1
2
=
4x
2
+
4x
+
1
Square of a Binomial –
Square of a Sum
5.2 Multiplication of Polynomials
Square of a Binomial –
Square of a Difference
5.2 Multiplication of Polynomials
Use the formula
(a  b)
2
=
a
2

2ab
+
b
2
(4m  5)
2
=
(4m  5)(4m  5)
where
a
= 4m
and
b
= 5
, then
(4m  5)
2
=
(4m)
2

2(4m)(5)
+
5
2
=
16m
2
–
40m
+
25
Product of a Sum and Difference
5.2 Multiplication of Polynomials
Use the formula
(a + b)(a  b) =
a
2
 b
2
(2z + 5k
4
)(2z – 5k
4
)
where
a
= 2z
and
b
= 5k
4
, then
(2z + 5k
4
)(2z – 5k
4
) =
(2z)
2
– (5k
4
)
2
=
4z
2
– 25k
8
Product of a Sum and Difference
5.2 Multiplication of Polynomials
Use the formula
(a + b)(a  b) =
a
2
 b
2
3rt(r – 2t)(r + 2t)
where
a
= r
and
b
= 2t
, then
3rt(r – 2t)(r + 2t)
=
3rt[
r
2
– (2t)
2
]
= 3rt(r
2
– 4t
2
)
= 3r
3
t – 12rt
3
5.1 Polynomial Functions
Multiplying polynomial functions:
Evaluate
f(3)
and
g(3)
and multiply the results.
4
)
(
Let
3
2
)
(
Let
2
2
x
x
g
x
x
x
f
).
)(
(
and
)
3
)(
(
Find
x
fg
fg
117
13
9
)
3
)(
(
13
4
3
)
3
(
9
9
18
)
3
(
3
)
3
(
2
)
3
(
)
3
)(
(
2
2
fg
g
f
fg
x
x
x
x
x
x
x
x
x
x
x
x
fg
x
x
g
x
x
x
f
x
fg
12
8
3
2
12
3
8
2
)
4
)(
3
2
(
)
)(
(
4
)
(
3
2
)
(
)
)(
(
2
3
4
3
2
4
2
2
2
2
5.5 Special Types
of Factoring
5.4 Factoring
Trinomials
5.3 Factoring
Polynomials
5. 2 Multiplication of
Polynomials
5.1 Polynomial
Functions
5.7 Factoring
Equations
Chapter 5 – Polynomial Expressions and Functions
Find the GCF for the following monomials using prime factorization.
Each monomial has
2, 3, x, y, y
in common.
Multiply the common factors to get the GCF of
6xy
2
.
5.3 Factoring Polynomials
Finding the Greatest Common Factor (GCF)
y
y
x
xy
y
y
x
x
x
y
x
y
y
y
x
x
y
x
3
3
2
18
3
2
2
2
24
3
3
2
2
36
2
2
3
3
2
When factoring an expression, find the GCF for each term
or
monomial
and put the remaining expression in parenthesis.
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 Fall '13
 Factoring, Distributive Property, Quadratic equation, Elementary algebra, GCFs