Question

Write a pair of factors that have the given product. $$49 x^{2}-169$$

Short answer

The pair of factors for the given product \(49x^{2} - 169\) are (7x - 13) and (7x + 13).

Step-by-step solution

Identify a and b

In the formula \(a^{2} - b^{2} = (a - b)(a + b)\), identify \(a^{2} = 49x^{2}\) and \(b^{2} = 169\) in the exercise expression. So, \(a = 7x\) and \(b = 13\).

Apply formula

Insert the values of a and b into the formula to get the pair of factors. That will yield, \(a - b = 7x - 13\) and \(a + b = 7x + 13\).

Write the expression

Rewrite the exercise expression as \((7x - 13)(7x + 13)\). Pair of factors that have the given product are (7x - 13) and (7x + 13).