Questions: Factor the difference of squares. 49-16 z^2

Solution Steps

The given expression is \(49 - 16z^2\). This can be recognized as a difference of squares because it is in the form \(a^2 - b^2\), where \(a^2 = 49\) and \(b^2 = 16z^2\).

To apply the difference of squares formula, we need to find \(a\) and \(b\):

• \(a^2 = 49\) implies \(a = \sqrt{49} = 7\).
• \(b^2 = 16z^2\) implies \(b = \sqrt{16z^2} = 4z\).

The difference of squares formula is given by: \[ a^2 - b^2 = (a - b)(a + b) \] Substituting the values of \(a\) and \(b\) into the formula, we have: \[ 49 - 16z^2 = (7 - 4z)(7 + 4z) \]

Final Answer