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Math 90
4.6 "Multiplying Polynomials"
Objectives:
*
Multiply polynomials.
*
Find special products.
*
Use multiplication to simplify expressions.
Multiplying Monomials
Multiplying Monomials:
kTo multiply two monomials, multiply the numerical factors (the coe¢ cients) and then multiply the variable factors.k
Example 1: (Multiplying monomials)
Multiply the following monomials.
a)
2y 3
4y 2
b)
5ab3 c ( 3abc) 6a2 b2 c2
Multiply a Polynomial by a Monomial
Multiplying Polynomials by Monomials
kTo multiply a monomial and a polynomial, multiply each term of the polynomial by the monomial.k
Example 2: (Multiplying a polynomial by a monomial)
Multiply the following expressions.
a) 3x2 5x6 + 4x2
b)
2ab2 3a3 b
2a2 b + 4b2
Multiply Two Binomials
Example 3: (Multiplying two binomials)
Multiply the following binomials.
a) (3x + 4) (2x
9)
b)
Page: 1
5y 2
4
1 + 2y 2
Notes by Bibiana Lopez
Beginning and Intermediate Algebra by Gustafson and Frisk
4.6
The FOIL Method
The FOIL Method:
To multiply two binomials, A + B and C + D :
Step 1: Multiply First terms:
Step 2: Multiply Outside terms:
=)
(A + B) (C + D) =
Step 3: Multiply Inside terms:
Step 4: Multiply Last terms:
Example 4: (Using the FOIL method)
Multiply the following polynomials:
a) (x + 4) (x
c) (1 + 2x) (1
4)
3x)
b)
d)
2x2
w+
3
3
4
x3
w+
2
3
4
Special Products:
2
(x + y) =
(x
2
y) =
(x + y) (x
y) =
Page: 2
Notes by Bibiana Lopez
Beginning and Intermediate Algebra by Gustafson and Frisk
4.6
Example 5: (Special products)
Find each product:
a) (2a
2
2
3b)
d) (x + 2y)
c) (4x + 5y) (4x
5y)
Multiply Any Two Polynomials
Multiplying Polynomials
To multiply two polynomials, multiply each term of one polynomial by each term of the other polynomial,
and then combine like terms.
Example 6: (Multiplying polynomials)
Multiply the following polynomials.
a)
3y 2 + y
4y 2
b) (2a + b) 3a2
2y + 5
4ab
b2
Multiply Three Polynomials
Example 7: (Multiplying three polynomials)
Multiply the following polynomials.
a)
2r (r
2s) (5r
4s)
b) (2x
Page: 3
3
y)
Notes by Bibiana Lopez
Beginning and Intermediate Algebra by Gustafson and Frisk
4.6
Multiply Binomials to Solve Equation
Example 8: (Solve equations)
Solve:
a) (y
5) (y
2) = y 2
4
b) (x + 2) (x
Page: 4
4) = (x + 6) (x
3)
Notes by Bibiana Lopez