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Chapter 0: Problem 40

Factor the difference of two squares. $$x^{2}-144$$

Short Answer

Expert verified
The factorized form of the difference of two squares \(x^{2}-144\) is \((x - 12)(x + 12)\).

Step by step solution

01

Identify 'a' and 'b' from the expression

In the expression \(x^{2}-144\), \(a\) is clearly \(x\) and \(b\) can be identified as 12, since \(12^{2} = 144\).
02

Apply the difference of squares pattern

The difference of squares pattern can be written as \(a^{2} - b^{2} = (a - b)(a + b)\). Substitute \(a\) with \(x\) and \(b\) with 12.
03

Evaluate the result

On substituting the values of 'a' and 'b', we get $(x - 12)(x + 12)$. Hence, the factorized form of the difference of two squares \(x^{2}-144\) is \((x - 12)(x + 12)\).

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