Explain how to factor 5x^2 - 125.
5x^2 - 125.
= 5(x^2 - 25)
= 5(x+5)(x-5)
To factor the expression 5x^2 - 125, you can first notice that both terms have a common factor of 5. By factoring out the common factor, you get:
5x^2 - 125 = 5(x^2 - 25)
Now, you can observe that the expression within the parentheses, x^2 - 25, is a difference of squares. A difference of squares can be factored as follows:
a^2 - b^2 = (a + b)(a - b)
Using this formula, you can rewrite x^2 - 25 as (x + 5)(x - 5). Therefore, the factored form of 5x^2 - 125 is:
5(x + 5)(x - 5)
To summarize:
1. Start by factoring out the common factor of 5 from both terms: 5x^2 - 125 = 5(x^2 - 25)
2. Recognize that x^2 - 25 is a difference of squares.
3. Use the formula for the difference of squares: a^2 - b^2 = (a + b)(a - b)
4. Rewrite x^2 - 25 as (x + 5)(x - 5).
5. Combine everything: 5(x + 5)(x - 5) is the factored form of 5x^2 - 125.