Problem 40 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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

Step 1 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.

Step 2 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.

Step 3 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 \((x + 12)(x - 12)\).