Yes, x² + 4x + 4 is a perfect square trinomial. A perfect square trinomial is a polynomial that can be expressed as the square of a binomial. In this case, you can factor x² + 4x + 4 into (x + 2)².
To see why this is the case, we can use the formula for a perfect square trinomial:
- (a + b)² = a² + 2ab + b²
By identifying a and b in our polynomial:
- a = x
- b = 2
We can see that:
- a² = x²
- 2ab = 2(x)(2) = 4x
- b² = 2² = 4
This confirms that when we combine them, we indeed get:
x² + 4x + 4 = (x + 2)²
Therefore, x² + 4x + 4 is definitely a perfect square trinomial.