January 18, 2017
Lesson 5.5
Multiplying Polynomials; Special Products
We have already learned how to multiply
two monomials such as
=
To multiply a polynomial by a monomial, use the
distributive property to multiply each term in
the polynomial by the monomial.
6
4
6x - 15x + 21x
2
Now try these!
4
5
36x - 28x + 12x
5
3
3 4 4
3
4 5 5
-15x yz + 12x y z - 24x y z
3
2
3
2
3
15x - 40x - 6x + 14x = 9x - 26x
2
.
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January 18, 2017
To multiply two polynomials, multiply each term in the
second polynomial by each term in the first polynomial.
Then combine like terms.
We can multiply two binomials together
using the distributive property twice.
First distribute 5x over (2x - 9) then distribute 1 over (2x - 9).
2
10x - 45x + 2x - 9
2
10x - 43x - 9
.
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January 18, 2017
Now try these on your own!
2
= x + 8x - 5x - 40
2
= x + 3x - 40
FO
2
= 12x - 30x - 14x + 35
2
= 12x - 44x + 35
I L
2
2
= 3x + 7xy + 12xy + 28y
2
2
= 3x + 19xy + 28y
F O I L
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r
n
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a
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Multiplying a binomial and trinomial.
We distribute each term in the binomial over
each term in the trinomial and simplify the result.
2
2
3
= x - 5x + 4x - 3x + 15x - 12
3
2
= x - 8x + 19x - 12
.
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January 18, 2017
Try these on your own!
3
2
2
= 12x + 4x - 8x - 15x - 5x + 10
3
2
= 12x - 11x - 13x + 10
4
3
2
3
2
2
= x + 4x - 2x + 7x + 28x - 14x + 5x + 20x - 10
4
3
2
= x + 11x + 31x + 6x - 10
You may find it easier to multiply this last problem vertically.
.
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January 18, 2017
Consider
Binomials that differ only in the sign separating
the terms are called conjugates:
a + b and a - b are conjugates.
The product of conjugates results in
a difference of two perfect squares.
For example:
2
2
2
(5x) - (3) = 25x - 9
Try these on your own!
2
x - 36
2
4y - 49
2
2
16x - 81y
.
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January 18, 2017
Squaring a Binomial
If a and b are real numbers, variables, or
expressions, then
, and
For example:
Try these yourself.
2
9x + 24x + 16
2
4y - 44y + 121
49 - 42z + 9z
2
.
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January 18, 2017
Lesson 5.5 pages 387-388.
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January 18, 2017
108)
r
r-2
109)
8