Questions: Factor. 81 a^2-25 81 a^2-25= (Factor completely.)

Transcript text: Factor. \[ 81 a^{2}-25 \] $81 a^{2}-25=$ $\square$ (Factor completely.)

Solution

Solution Steps

To factor the expression $81a^2 - 25$, recognize it as a difference of squares. The difference of squares formula is $x^2 - y^2 = (x - y)(x + y)$. Here, $81a^2$ is $(9a)^2$ and $25$ is $5^2$. Thus, the expression can be factored using this formula.

Step 1: Identify the Expression

We start with the expression $81a^2 - 25$.

Step 2: Recognize the Difference of Squares

This expression can be recognized as a difference of squares, which follows the formula: \[ x^2 - y^2 = (x - y)(x + y) \] In our case, we have: \[ x = 9a \quad \text{and} \quad y = 5 \]

Step 3: Apply the Difference of Squares Formula

Using the difference of squares formula, we can factor the expression: \[ 81a^2 - 25 = (9a - 5)(9a + 5) \]