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Chapter 0: Problem 94

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 formula used to find the product of the sum and difference of two terms is \(a^2 - b^2 = (a + b)(a - b)\). In our example, we chose 3 for a, and 2 for b, and validated that the equation holds when applying these chosen values.

Step by step solution

01

Understanding the formula

The formula to find the product of the sum and difference of two terms, also known as the difference of squares, is \(a^2 - b^2 = (a + b)(a - b)\), where \(a\) and \(b\) are the two terms.
02

Chose example values

To provide a concrete example, let's take \(a = 3\) and \(b = 2\) as our two terms.
03

Applying the formula

Let's substitute the numbers into the formula: \((3 + 2)(3 - 2) = 3^2 - 2^2\). This results in `5*1 = 9 - 4`.
04

Solving the equation

By simplifying each side of the equality, we get `5 = 5`. As you can see, both sides are equal which indicates our formula is correctly applied.

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