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Chapter 0: Problem 41

Factor the difference of two squares. $$36 x^{2}-49$$

Short Answer

Expert verified
The factorized form of \(36x^2 - 49\) is \((6x + 7)(6x - 7)\).

Step by step solution

01

Identify the expression as a difference of squares

In the given exercise \(36x^2 - 49\), it can be seen that this is a difference of squared entities. Where \(36x^2\) can be represented as \((6x)^2\) and \(49\) can be represented as \((7)^2\). So, the expression can be written as \((6x)^2 - (7)^2\).
02

Apply the formula for difference of squares

Applying the formula \(a^{2} - b^{2} = (a+b)(a鈭抌)\) on the given expression, where \(a = 6x\) and \(b = 7\), the expression should be rewritten as \((6x + 7)(6x - 7)\).

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Most popular questions from this chapter

What does \(a^{\frac{m}{n}}\) mean?

Factor completely. $$2 x^{2}-7 x y^{2}+3 y^{4}$$

Factor Completely. $$(x+y)^{4}-100(x+y)^{2}$$

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. $$\frac{x^{2}+6 x+5}{x^{2}-25}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$5+3(x-4)=8(x-4)=8 x-32$$
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