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Chapter 0: Problem 32

Find each product. $$(x+5)(x-5)$$

Short Answer

Expert verified
The product of the expressions \((x+5)(x-5)\) equals to: \(x^2 - 25\).

Step by step solution

01

Recognizing The Product Pattern

First, note that this problem can be solved using the formula for the difference of squares. The difference of squares formula is: \(a^2-b^2 = (a+b)(a-b)\). In the exercise, however, the form is applied in reverse, the term \(x\) takes the place of \(a\) and \(5\) takes place of \(b\).
02

Apply The Product

Applying the values of \(a\) and \(b\) to the difference of squares formula will give: \((a+b)(a-b) = a^2 - b^2\). Substituting the values from the equation, \(x + 5\) for \(a+b\) and \(x - 5\) for \(a-b\), you get the product: \(x^2 - 5^2\).
03

Solving The Expression

The last step is to finish the calculation. Square the current \(b\) which is \(5\) to get \(25\). Thus you get: \(x^2 - 25\) as result.

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Most popular questions from this chapter

Evaluate each expression. $$\sqrt[3]{\sqrt[4]{16}+\sqrt{625}}$$

Will help you prepare for the material covered in the next section.Exercises \(144-146\) will help you prepare for the material covered in the next section. Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$ \frac{x^{2}+6 x+5}{x^{2}-25} $$

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