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13-5 Multiplying Polynomials by Monomials
February 24, 2011February 24, 2011
Pre-Algebra
Warm UpMultiply. Write each product as one power.
1. x · x2. 62 · 63
3. k2 · k8
4. 195 · 192
5. m · m5
6. 266 · 265
7. Find the volume of a rectangular prism that measures 5 cm by 2 cm by 6 cm.
x2
65
k10
13-5 Multiplying Polynomials by Monomials
197
m6
2611
60 cm3
Pre-Algebra
Remember that when you multiply two powers with the same bases, you add the exponents.
(5m2n3)(6m3n6)
5 · 6 · m2+3n3+6
30m5n9
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
To multiply two monomials, multiply the coefficients and add the exponents of the variables that are the same.
Multiply.
Multiplying Monomials
A. (2x3y2)(6x5y3)
(2x3y2)(6x5y3)
12x8y5
Multiply coefficients and addexponents.
B. (9a5b7)(–2a4b3)
(9a5b7)(–2a4b3)
–18a9b10
Multiply coefficients and addexponents.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Try This
Insert Lesson Title Here
Multiply.
A. (5r4s3)(3r3s2)
(5r4s3)(3r3s2)
15r7s5
Multiply coefficients and addexponents.
B. (7x3y5)(–3x3y2)
(7x3y5)(–3x3y2)
–21x6y7
Multiply coefficients and addexponents.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
To multiply a polynomial by a monomial, use the Distributive Property.
Multiply every term of the polynomial by the monomial.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Multiply.
Multiplying a Polynomial by a Monomial
A. 3m(5m2 + 2m)
3m(5m2 + 2m)
15m3 + 6m2
Multiply each term in parentheses by 3m.
B. –6x2y3(5xy4 + 3x4)
–6x2y3(5xy4 + 3x4)
–30x3y7 – 18x6y3
Multiply each term in parentheses by –6x2y3.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Multiply.
Multiplying a Polynomial by a Monomial
C. –5y3(y2 + 6y – 8)
–5y3(y2 + 6y – 8)
–5y5 – 30y4 + 40y3
Multiply each term in parentheses by –5y3.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Try This: Example 2A & 2B
Multiply.
Insert Lesson Title Here
A. 4r(8r3 + 16r)
4r(8r3 + 16r)
32r4 + 64r2
Multiply each term in parentheses by 4r.
B. –3a3b2(4ab3 + 4a2)
–3a3b2(4ab3 + 4a2)
–12a4b5 – 12a5b2
Multiply each term in parentheses by –3a3b2.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Example 2
Insert Lesson Title Here
Multiply.
C. –2x4(x3 + 4x + 3)
–2x4(x3 + 4x + 3)
–2x7 – 8x5 – 6x4
Multiply each term in parentheses by –2x4.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Get out your Agenda
• Tonight’s Assignment
– Page 666 # 10-19
Lesson QuizMultiply.
1. (3a2b)(2ab2)
2. (4x2y2z)(–5xy3z2)
3. 3n(2n3 – 3n)
4. –5p2(3q – 6p)
5. –2xy(2x2 + 2y2 – 2)
–20x3y5z3
6a3b3
Insert Lesson Title Here
6n4 – 9n2
–15p2q + 30p3
Pre-Algebra
–4x3y – 4xy3 + 4xy
13-5 Multiplying Polynomials by Monomials
