Question: Factor. $64c^2 - 25$ $64c^2 - 25 = \boxed{\phantom{Factor completely.}}$ (Factor completely.)

Factor.

$64c^2 - 25$

$64c^2 - 25 = \boxed{\phantom{Factor completely.}}$ (Factor completely.)

Solution

To factor the expression \(64c^2 - 25\), we recognize it as a difference of squares. The formula for factoring a difference of squares is: \[ a^2 - b^2 = (a - b)(a + b) \] First, identify \(a^2\) and \(b^2\): \[ a^2 = 64c^2 \] \[ b^2 = 25 \] Calculate \(a\) and \(b\): \[ a = \sqrt{64c^2} = 8c \] \[ b = \sqrt{25} = 5 \] Now apply the difference of squares formula: \[ 64c^2 - 25 = (8c - 5)(8c + 5) \] Thus, the completely factored expression is: \[ (8c - 5)(8c + 5) \]