Questions: Factor the expression. (Factor your answer completely.) 8x^2-18

Solution Steps

To factor the given expression \(8x^2 - 18\), we can follow these steps:

1. Identify the greatest common factor (GCF) of the terms.
2. Factor out the GCF.
3. Check if the remaining expression can be factored further.

First, we identify the greatest common factor (GCF) of the terms in the expression \(8x^2 - 18\). The GCF of 8 and 18 is 2.

Next, we factor out the GCF from the expression: \[ 8x^2 - 18 = 2(4x^2 - 9) \]

The remaining expression inside the parentheses, \(4x^2 - 9\), is a difference of squares. We can factor it further using the formula \(a^2 - b^2 = (a - b)(a + b)\): \[ 4x^2 - 9 = (2x)^2 - 3^2 = (2x - 3)(2x + 3) \]

Combining all the factors, we get: \[ 8x^2 - 18 = 2(2x - 3)(2x + 3) \]

Final Answer