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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Question
![**Addition of Polynomials:**
We are tasked with adding the following polynomials:
\[
(5x^4y^2 - x^2y^2 + 12xy) + (-6x^4y^2 - 6x^2y - 11xy)
\]
**Steps to Solve:**
1. **Combine like terms** from each polynomial.
2. The like terms are:
- \( x^4y^2 \) terms: \( 5x^4y^2 \) and \(-6x^4y^2\)
- \( x^2y^2 \) term: \(-x^2y^2\)
- \( xy \) terms: \( 12xy \) and \(-11xy\)
- \( x^2y \) term: \(-6x^2y\)
**Solution:**
1. Add the \( x^4y^2 \) terms:
\[
5x^4y^2 + (-6x^4y^2) = -x^4y^2
\]
2. The only \( x^2y^2 \) term:
\[
-x^2y^2
\]
3. Add the \( xy \) terms:
\[
12xy + (-11xy) = xy
\]
4. The only \( x^2y \) term:
\[
-6x^2y
\]
**Final Simplified Sum:**
The sum is:
\[
-x^4y^2 - x^2y^2 + xy - 6x^2y
\]
**Note:** Always ensure like terms (terms with the same variables raised to the same powers) are combined to simplify polynomial expressions effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6dc9660-7620-4f4d-948a-9c83904c3782%2F86016dbc-13b1-425a-baec-314f15a58123%2Fbb1lzm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Addition of Polynomials:**
We are tasked with adding the following polynomials:
\[
(5x^4y^2 - x^2y^2 + 12xy) + (-6x^4y^2 - 6x^2y - 11xy)
\]
**Steps to Solve:**
1. **Combine like terms** from each polynomial.
2. The like terms are:
- \( x^4y^2 \) terms: \( 5x^4y^2 \) and \(-6x^4y^2\)
- \( x^2y^2 \) term: \(-x^2y^2\)
- \( xy \) terms: \( 12xy \) and \(-11xy\)
- \( x^2y \) term: \(-6x^2y\)
**Solution:**
1. Add the \( x^4y^2 \) terms:
\[
5x^4y^2 + (-6x^4y^2) = -x^4y^2
\]
2. The only \( x^2y^2 \) term:
\[
-x^2y^2
\]
3. Add the \( xy \) terms:
\[
12xy + (-11xy) = xy
\]
4. The only \( x^2y \) term:
\[
-6x^2y
\]
**Final Simplified Sum:**
The sum is:
\[
-x^4y^2 - x^2y^2 + xy - 6x^2y
\]
**Note:** Always ensure like terms (terms with the same variables raised to the same powers) are combined to simplify polynomial expressions effectively.
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