27p^2 - 48q^2
3(9p^2-16q^2)
= 3((3p)^2 - (4q)^2)
now, what do you know about a^2 - b^2 ?
To simplify the expression 27p^2 - 48q^2, you can first look for any common factors between the terms. In this case, both terms have a common factor of 3.
So, we can rewrite the expression as follows:
27 p^2 - 48 q^2 = 3 (9 p^2 - 16 q^2)
Now let's focus on simplifying the expression within the parentheses, 9p^2 - 16q^2. Notice that it is a difference of squares with p^2 and q^2 as perfect squares.
We can use the formula for the difference of squares, which states that a^2 - b^2 = (a + b)(a - b).
In this case, a = 3p and b = 4q. Applying the formula, we have:
9p^2 - 16q^2 = (3p + 4q)(3p - 4q)
So, the simplified expression for 27p^2 - 48q^2 is 3(3p + 4q)(3p - 4q).