Identify this polynomial as a perfect square trinomial, a difference of squares, or neither.
9a^2+9a+36
Is it difference of squares?
a perfect square trinomial
It is neither a perfect square trinomial nor a difference of squares.
To determine whether the given polynomial is a difference of squares, we need to check if it can be factored in the form (x^2 - y^2), where x and y are terms.
The given polynomial is 9a^2 + 9a + 36. Let's examine each term individually:
- The first term, 9a^2, can be factored as (3a)^2.
- The last term, 36, can be factored as (6)^2.
If we try to find the square root of the middle term, 9a, it does not simplify to an integer. Therefore, we cannot express this polynomial as a difference of squares.
In conclusion, the polynomial 9a^2 + 9a + 36 is neither a perfect square trinomial nor a difference of squares.
9(a^2+a+4)
Answer: Neither.
Difference of 2 squares = (a+b)(a-b) =
a^2 - b^2