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Chapter 5: Problem 104

Explain how to find the product of the sum and difference of two terms. Give an example with your explanation.

Short Answer

Expert verified
The product of the sum and the difference of two terms can be obtained by using the identity \(a^2 - b^2 = (a+b) \cdot (a-b)\). An example is given with the terms a = 3 and b = 2, resulting in a product of 5.

Step by step solution

01

Understand the mathematical identity

The identity \(a^2 - b^2 = (a+b) \cdot (a-b)\) states that the difference of the squares of any two terms is equal to the product of the sum and the difference of these two terms. This identity is derived from the property of real numbers.
02

Apply the Identity

To find the product of the sum and difference of two terms a and b, simply apply the identity. That means find the sum (a+b) and the difference (a-b) of the two terms, and then multiply these two quantities together.
03

Example

Suppose a = 3 and b = 2. The sum of these terms is a+b = 5 and the difference is a-b = 1. Therefore, the product of the sum and difference is (5)*(1) = 5, which is equal to the difference of the squares of the two terms: \(a^2 - b^2 = 3^2 - 2^2 = 5\)

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Most popular questions from this chapter

Exercises \(110-112\) will help you prepare for the material covered in the next section. In each exercise, perform the long division without using a calculator, and then state the quotient and the remainder. $$. 9 8 \longdiv { 2 5 . 1 8 7 }$$

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Simplify: \(24+8 \cdot 3+28 \div(-7)\).

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