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Chapter 0: Problem 42

Factor the difference of two squares. $$64 x^{2}-81$$

Short Answer

Expert verified
The factored form of the difference of squares \(64x^{2}-81\) is \((8x+9)(8x-9)\).

Step by step solution

01

Identify the square roots

The first step is to determine the square roots of both 64x^2 and 81. So, \(\sqrt{64x^{2}} = 8x\) and \(\sqrt{81} = 9\).
02

Apply the formula

Now, using the formula \(a^{2} - b^{2} = (a+b)(a-b)\), where \(a=8x\) and \(b=9\), apply the formula to the difference of squares.
03

Carry out the operation

Substitute \(a\) and \(b\) into the formula. This gives \((8x+9)(8x-9)\).

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Most popular questions from this chapter

Write a quadratic equation in general form whose solution set is \(\\{-3,5\\}\).

Find \(b\) such that \(\frac{7 x+4}{b}+13=x\) will have a solution set given by \(\\{-6\\}\).

Describe the solution set of \(|x|>-4\)

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$ 2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right) $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$\frac{7 x}{x+3}+\frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\).
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