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Chapter 0: Problem 100

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 two terms \(a\) and \(b\) (where \(a > b\)) is given by the formula \(a^2 - b^2\). An example using a=5, b=3 verifies this formula. The process involves first calculating the sum \((a + b)\) and difference \((a - b)\) of the terms, then multiplying them together to find the product.

Step by step solution

01

Understand the Terms and Identify their Sum and Difference

Firstly, let's consider two algebraic terms, let these be a and b. Their sum is given by \(a + b\), and difference by \(a - b\).
02

Compute the Product of the Sum and Difference

Now we compute the product of the sum and difference of these terms, that is, we multiply \((a + b)\) with \((a - b)\). Using this formula: \((a + b)(a - b) = a^2 - b^2\), we see that the product is \(a^2 - b^2\).
03

Verification with an example

To confirm the formula, let鈥檚 substitute a and b each with numerical values. Let a = 5 and b = 3. Hence, \((a + b)(a - b) = (5 + 3)(5 - 3) = 8 * 2 = 16\). And while calculating \(a^2 - b^2\) we have \(5^2 - 3^2 = 25 - 9 = 16\). Both show that they are equal, so their multiplication gives the same result.

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