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Chapter 7: Problem 51

Multiply and simplify each of the following. Whenever possible, do the multiplication of two binomials mentally. $$(2 r-s)(r+3 s)$$

Short Answer

Expert verified
2r^2 + 5rs - 3s^2

Step by step solution

01

- Distribute each term

To multiply \( (2r - s)(r + 3s) \), use the distributive property (also known as the FOIL method for binomials): first multiply each term of the first binomial by each term of the second binomial.
02

- Multiply First Terms

Multiply the first terms: \(2r \cdot r = 2r^2 \).
03

- Multiply Outer Terms

Multiply the outer terms: \(2r \cdot 3s = 6rs \).
04

- Multiply Inner Terms

Multiply the inner terms: \(-s \cdot r = -sr \), which is also written as \(-rs \).
05

- Multiply Last Terms

Multiply the last terms: \(-s \cdot 3s = -3s^2 \).
06

- Combine Like Terms

Combine all the terms: \(2r^2 + 6rs - rs - 3s^2 \). Next, combine the like terms \(6rs \) and \(-rs \): \(6rs - rs = 5rs \). Thus, the expression simplifies to \(2r^2 + 5rs - 3s^2 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

distributive property