Questions: 25c^2-144 = (Factor completely.)

Transcript text: \[ 25 c^{2}-144 \] $25 c^{2}-144=$ $\square$ (Factor completely.)

Solution

Solution Steps

To factor the given expression $25c^2 - 144$, we recognize it as a difference of squares. The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$. Here, $25c^2$ is $(5c)^2$ and $144$ is $12^2$. So, we can apply the formula directly.

Step 1: Recognize the Expression as a Difference of Squares

The given expression is $25c^2 - 144$. We recognize this as a difference of squares, which can be factored using the formula: \[ a^2 - b^2 = (a - b)(a + b) \]

Step 2: Identify $a$ and $b$

In the expression $25c^2 - 144$: \[ 25c^2 = (5c)^2 \quad \text{and} \quad 144 = 12^2 \] Thus, we have $a = 5c$ and $b = 12$.

Step 3: Apply the Difference of Squares Formula

Using the difference of squares formula: \[ 25c^2 - 144 = (5c)^2 - 12^2 = (5c - 12)(5c + 12) \]