Completely factor the expression 4q2 27r4?

Answer 1

To factor the expression 4q^2 - 27r^4, we first note that this is a difference of squares, as 4q^2 is (2q)^2 and 27r^4 is (3r^2)^3. Therefore, we can rewrite the expression as (2q)^2 - (3r^2)^2. This can be factored further using the difference of squares formula, resulting in (2q + 3r^2)(2q - 3r^2) as the completely factored form.

Answer 2

Let's take a moment to appreciate the beauty of this expression. We can see that it is a difference of squares, with 4q^2 being the square of 2q and 27r^4 being the square of 3r^2. So, when we factor it completely, we get (2q + 3r^2)(2q - 3r^2). Just like painting a happy little tree, factoring can be a peaceful process if we take it one step at a time.

Answer 3

2 x 2 x q x q x 3 x 3 x 3 x r x r x r x r