Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.4: Special Products
Problem 60HP
Related questions
Question
![### Multiplication of Binomials
**Problem: Multiply the given binomials.**
\[ (4x - 1)(3x - 2) \]
Which of the following is the correct product?
- a) \( 11x - 12 \)
- b) \( 12x - 11 \)
- c) \( 12x^2 + 11x - 2 \)
- d) \( 12x^2 - 11x + 2 \)
- e) \( 11x^2 - 12x + 1 \)
To find the product, use the distributive property (also known as the FOIL method for multiplying two binomials):
### Step-by-Step Solution:
1. **First Terms:**
\[
(4x) \cdot (3x) = 12x^2
\]
2. **Outer Terms:**
\[
(4x) \cdot (-2) = -8x
\]
3. **Inner Terms:**
\[
(-1) \cdot (3x) = -3x
\]
4. **Last Terms:**
\[
(-1) \cdot (-2) = 2
\]
5. **Combine Like Terms:**
\[
12x^2 - 8x - 3x + 2 = 12x^2 - 11x + 2
\]
Thus, the correct product is:
\[
\boxed{12x^2 - 11x + 2}
\]
The correct answer is:
- d) \( 12x^2 - 11x + 2 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfa510ce-a779-4198-b3d3-c9e941c192c9%2Fcb909bd1-4e02-44ba-8fdf-b16099466cae%2Fx3cilih_processed.png&w=3840&q=75)
Transcribed Image Text:### Multiplication of Binomials
**Problem: Multiply the given binomials.**
\[ (4x - 1)(3x - 2) \]
Which of the following is the correct product?
- a) \( 11x - 12 \)
- b) \( 12x - 11 \)
- c) \( 12x^2 + 11x - 2 \)
- d) \( 12x^2 - 11x + 2 \)
- e) \( 11x^2 - 12x + 1 \)
To find the product, use the distributive property (also known as the FOIL method for multiplying two binomials):
### Step-by-Step Solution:
1. **First Terms:**
\[
(4x) \cdot (3x) = 12x^2
\]
2. **Outer Terms:**
\[
(4x) \cdot (-2) = -8x
\]
3. **Inner Terms:**
\[
(-1) \cdot (3x) = -3x
\]
4. **Last Terms:**
\[
(-1) \cdot (-2) = 2
\]
5. **Combine Like Terms:**
\[
12x^2 - 8x - 3x + 2 = 12x^2 - 11x + 2
\]
Thus, the correct product is:
\[
\boxed{12x^2 - 11x + 2}
\]
The correct answer is:
- d) \( 12x^2 - 11x + 2 \)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![PREALGEBRA](https://www.bartleby.com/isbn_cover_images/9781938168994/9781938168994_smallCoverImage.gif)
![Elementary Algebra](https://www.bartleby.com/isbn_cover_images/9780998625713/9780998625713_smallCoverImage.jpg)
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![PREALGEBRA](https://www.bartleby.com/isbn_cover_images/9781938168994/9781938168994_smallCoverImage.gif)
![Elementary Algebra](https://www.bartleby.com/isbn_cover_images/9780998625713/9780998625713_smallCoverImage.jpg)
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9780998625720/9780998625720_smallCoverImage.gif)
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell