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Chapter 7: Problem 53

Factor: \(25 x^{2}-81 .\) (Section 6.4, Example 1)

Short Answer

Expert verified
The factored form of \(25x^{2}-81\) is \((5x - 9)(5x + 9)\).

Step by step solution

01

Identify the Difference of Squares

A binomial is a difference of squares if it can be written in the form \(a^{2}-b^{2}\), where \(a\) and \(b\) are real numbers. In the expression \(25x^{2}-81\), we can rewrite it as \((5x)^{2} - (9)^{2}\). This confirms that the exercise is a difference of squares.
02

Factor using the Difference of Squares Formula

The formula for factoring the difference of squares is \(a^{2} - b^{2} = (a - b)(a + b)\). Applying this formula on \((5x)^{2} - (9)^{2}\), we get \((5x - 9)(5x + 9)\). This is the factored form of the given expression.

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Most popular questions from this chapter

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{11}{x+7}-\frac{5}{-x-7}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-1}{6}+\frac{x+2}{3}$$

If you can do a job in 6 hours and your friend can do the same job in 3 hours, explain how to find how long it takes to complete the job working together. It is not necessary to solve the problem.

add or subtract as indicated. Simplify the result, if possible. $$\frac{3 y^{2}-2}{3 y^{2}+10 y-8}-\frac{y+10}{3 y^{2}+10 y-8}-\frac{y^{2}-6 y}{3 y^{2}+10 y-8}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{x}+9$$
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