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Chapter 0: Problem 40

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

Short Answer

Expert verified
The difference of squares \(x^{2}-144\) can be factored into \((x+12)(x-12)\).

Step by step solution

01

Identify \(a\) and \(b\)

We must first identify what represents \(a\) and \(b\) in the expression. In the expression \(x^{2}-144\), \(a\) is \(x\) since \(x\) is being squared. \(b\) is \(12\) since \(144\) is the square of \(12\) and we have a minus sign between them, indicating that it's a difference of squares.
02

Apply the Difference of Squares Formula

Once we have identified \(a\) and \(b\), we must then substitute these values into the formula \(a^{2} - b^{2} = (a+b)(a-b)\), resulting in the factored form of the difference of squares.
03

Finalize the Solution

Replace \(a\) by \(x\) and \(b\) by \(12\) in the formula, so, the factored form will be \((x + 12)(x - 12)\). It indicates that the original difference of squares equation \(x^{2}-144\) could be factored into \((x + 12)(x - 12)\).

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