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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 difference of 5 and 3 is 16.

Step by step solution

01

Choose two terms

In this example, the terms 5 and 3 are chosen. These are represented as a and b respectively.
02

Find the Sum and Difference

Calculate the sum and difference of the two terms. The sum is \(5 + 3 = 8\) and the difference is \(5 - 3 = 2\).
03

Compute the Product

The product of the sum and difference of these two terms is calculated as \(8 * 2 = 16\).
04

Verify with the Algebraic Identity

Verify the product with the algebraic identity \(a^2 - b^2\). Here \(a = 5\) and \(b = 3\). Compute \(a^2 - b^2 = 25 - 9 = 16\) which is equal to the calculated product.
05

Conclusion

Thus, the product of the sum and difference of the numbers 5 and 3 is 16.

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