To find each product, we will multiply each term of the polynomial by the monomial. We use the distributive property to multiply a monomial and a polynomial. (a) Multiply each term of 3a2 За?(За?- 5а + 2) - 5a + 2 by 3a?. За? (За?) + За?(-5а) + За?(2) = 9aU- 15a3 +Oa? Distribute the multiplication by 3a2 Multiply the monomials. (b) Multiply each term of 6x³z + x²z² – xz³ + 7zª by -2xz³. -2xz (6x3z + x?z2 – xz³ + 7z*) - -2xz°(Ox³2) – 2xz°(x²z?) – 2xz°(-xz³) – 2xz°(Oz4) OX4A - 2x°z5 + 2x²z6 – D xz7 Multiply the monomials. (c) Multiply each term of -m4 – 25 by 4m3. (-mª – 25)(4m³) = -m*(4m³) –O (4m³) -Om? -Om3 Distribute the multiplication by 4m³. Multiply the monomials. Multiply: (a) 5c2(2c4 – 8c – 4) and (b) -s?t?(-s©rª + s$t5 – st6 + 4s) (a) (b)
To find each product, we will multiply each term of the polynomial by the monomial. We use the distributive property to multiply a monomial and a polynomial. (a) Multiply each term of 3a2 За?(За?- 5а + 2) - 5a + 2 by 3a?. За? (За?) + За?(-5а) + За?(2) = 9aU- 15a3 +Oa? Distribute the multiplication by 3a2 Multiply the monomials. (b) Multiply each term of 6x³z + x²z² – xz³ + 7zª by -2xz³. -2xz (6x3z + x?z2 – xz³ + 7z*) - -2xz°(Ox³2) – 2xz°(x²z?) – 2xz°(-xz³) – 2xz°(Oz4) OX4A - 2x°z5 + 2x²z6 – D xz7 Multiply the monomials. (c) Multiply each term of -m4 – 25 by 4m3. (-mª – 25)(4m³) = -m*(4m³) –O (4m³) -Om? -Om3 Distribute the multiplication by 4m³. Multiply the monomials. Multiply: (a) 5c2(2c4 – 8c – 4) and (b) -s?t?(-s©rª + s$t5 – st6 + 4s) (a) (b)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Polynomial Multiplication Using the Distributive Property
To find each product, we will multiply each term of the polynomial by the monomial.
We use the distributive property to multiply a monomial and a polynomial.
#### (a) Multiply \(3a^2(3a^2 - 5a + 2)\):
\[3a^2(3a^2 - 5a + 2)\]
1. **Distribute the multiplication by \(3a^2\)**:
\[= 3a^2(3a^2) + 3a^2(-5a) + 3a^2(2)\]
2. **Multiply the monomials**:
\[= 9a^4 - 15a^3 + 6a^2\]
#### (b) Multiply \(-2xz^3(6x^3z + x^2z^2 - xz^3 + 7z^4)\):
\(-2xz^3(6x^3z + x^2z^2 - xz^3 + 7z^4)\)
1. **Distribute the multiplication by \(-2xz^3\)**:
\[= -2xz^3(6x^3z) + -2xz^3(x^2z^2) + -2xz^3(-xz^3) + -2xz^3(7z^4)\]
2. **Multiply the monomials**:
\[= -12x^4z^4 - 2x^3z^5 + 2x^2z^6 - 14xz^7\]
#### (c) Multiply each term of \((-m^4 - 25)\) by \(4m^3\):
\((-m^4 - 25)(4m^3)\)
1. **Distribute the multiplication by \(4m^3\)**:
\[= -m^4(4m^3) - 25(4m^3)\]
2. **Multiply the monomials**:
\[= -4m^7 - 100m^3\]
#### Practice Problems:
1. Multiply \(5c^2(2c^4 - 8c - 4)\):
\[
\text{Answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c02ecae-9f3c-4011-90ce-878cb1c02c8e%2F75ca2eb3-060f-42ae-a6ea-829b17d3da28%2Fiqj383j_processed.png&w=3840&q=75)
Transcribed Image Text:### Polynomial Multiplication Using the Distributive Property
To find each product, we will multiply each term of the polynomial by the monomial.
We use the distributive property to multiply a monomial and a polynomial.
#### (a) Multiply \(3a^2(3a^2 - 5a + 2)\):
\[3a^2(3a^2 - 5a + 2)\]
1. **Distribute the multiplication by \(3a^2\)**:
\[= 3a^2(3a^2) + 3a^2(-5a) + 3a^2(2)\]
2. **Multiply the monomials**:
\[= 9a^4 - 15a^3 + 6a^2\]
#### (b) Multiply \(-2xz^3(6x^3z + x^2z^2 - xz^3 + 7z^4)\):
\(-2xz^3(6x^3z + x^2z^2 - xz^3 + 7z^4)\)
1. **Distribute the multiplication by \(-2xz^3\)**:
\[= -2xz^3(6x^3z) + -2xz^3(x^2z^2) + -2xz^3(-xz^3) + -2xz^3(7z^4)\]
2. **Multiply the monomials**:
\[= -12x^4z^4 - 2x^3z^5 + 2x^2z^6 - 14xz^7\]
#### (c) Multiply each term of \((-m^4 - 25)\) by \(4m^3\):
\((-m^4 - 25)(4m^3)\)
1. **Distribute the multiplication by \(4m^3\)**:
\[= -m^4(4m^3) - 25(4m^3)\]
2. **Multiply the monomials**:
\[= -4m^7 - 100m^3\]
#### Practice Problems:
1. Multiply \(5c^2(2c^4 - 8c - 4)\):
\[
\text{Answer
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