Question

How do you factor the expression `4x^2 - 25`?

Answer 1

See the entire explanation below:

Explanation:

This expression is in the form:

`a^2x^2 - b^2` and can be factored to:

`(sqrt(a^2x^2) - sqrt(b^2))(sqrt(a^2x^2) + sqrt(b^2))`

Substituting the values from the problem gives:

`4x^2 - 25 = 2^2x^2 - 5^2 = (sqrt(2^2x^2) - sqrt(5^2))(sqrt(2^2x^2) + sqrt(5^2)) =`

`(2x - 5)(2x + 5)`