Carson Elementary And Intermediate Algebra 3e
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Carson Elementary and Intermediate Algebra 3e
Section 5.5
Objectives
1.
Multiply a polynomial by a monomial.
2.
Multiply binomials
3.
Multiply polynomials
4.
Determine the product when given special polynomial factors.
Vocabulary
Conjugates
Binomials that differ only in the sign separating the terms.
Prior Knowledge
Multiply a monomial by a polynomial.
2
3
2
– a + 6)
– 5a
5a(2a
=
10a
+ 30a
3
3
2
6
5
3
– 2)
– 28w
- 4w
(3w
+ 7w
=
-12w
+ 8w
=
1
1
1
1
1
2
4
3
2
6
5
4
3
2
r 5
r
r
r
r
1
r 5
r
r
r
r 5
20
5
10
4
2
New Concepts
Multiplying binomials using FOIL: First + Outer + Inner + Last
2
2
(a + 4)(a + 9)
=
a
+ 4a + 9a + 36 = a
+ 13a + 36
2
(n + 7)(n – 5)
+ 2n – 35
=
n
2
(2t – 7)(3t – 1)
– 23t + 7
=
6t
Multiplying polynomials: multiply every term in the second polynomial by every term in the first polynomial.
Use either
horizontal
or
vertical
multiplication.
2
3
2
2
3
– 3x + 2)
– 3x
– 9x + 6 = x
– 7x + 6
(x + 3)(x
=
x
+ 2x + 3x
2
2
3
2
3
– 3fg – 9g
– 27fg
– 27g
(2f + 3g)(2f
)
=
4f
State the conjugate of the given binomial:
Binomial
Conjugate
x – 3
x + 3
2g – 3
2g + 3
2
2
Multiplying conjugates: (a + b)(a – b) = a
– b
.
2
2
(y + 4)(y – 4)
+ 4y – 4y – 16 = y
– 16
=
y
2
2
(4b – 5c)(4b + 5c)
– 25c
=
16b
V. Zabrocki 2011
page 1
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