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
Write the equation for each situation below showing that the area as a product is equal to the area as a sum.
![The expression provided is:
\( (3 - 5y)(2 + y) \)
To simplify this expression, apply the distributive property (also known as the FOIL method for binomials) as follows:
1. **First:** Multiply the first terms from each binomial.
\[
3 \times 2 = 6
\]
2. **Outer:** Multiply the outer terms from each binomial.
\[
3 \times y = 3y
\]
3. **Inner:** Multiply the inner terms from each binomial.
\[
-5y \times 2 = -10y
\]
4. **Last:** Multiply the last terms from each binomial.
\[
-5y \times y = -5y^2
\]
Combine all these results to get the expanded form:
\[
6 + 3y - 10y - 5y^2
\]
Simplify by combining like terms:
\[
6 - 7y - 5y^2
\]
The final simplified form of the expression is:
\[
-5y^2 - 7y + 6
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38b63a98-7e34-4a1a-8516-ff386264c8a3%2F05edd261-eceb-444f-8e21-52913725a094%2F67vlevg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The expression provided is:
\( (3 - 5y)(2 + y) \)
To simplify this expression, apply the distributive property (also known as the FOIL method for binomials) as follows:
1. **First:** Multiply the first terms from each binomial.
\[
3 \times 2 = 6
\]
2. **Outer:** Multiply the outer terms from each binomial.
\[
3 \times y = 3y
\]
3. **Inner:** Multiply the inner terms from each binomial.
\[
-5y \times 2 = -10y
\]
4. **Last:** Multiply the last terms from each binomial.
\[
-5y \times y = -5y^2
\]
Combine all these results to get the expanded form:
\[
6 + 3y - 10y - 5y^2
\]
Simplify by combining like terms:
\[
6 - 7y - 5y^2
\]
The final simplified form of the expression is:
\[
-5y^2 - 7y + 6
\]
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