Answer:
A perfect square trinomial is a trinomial expression of the form:
a^2 + 2ab + b^2
Where a and b are constants, it can also be written as (a + b)^2.
To identify a perfect square trinomial, we can check if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms.
For example, let's consider the expression:
x^2 + 4x + 4
The first term is x^2, which is a perfect square. The last term is 4, which is also a perfect square. The middle term is 4x, twice the product of the square roots of x^2 and 4 (i.e., 2x). Therefore, this expression is a perfect square trinomial:
x^2 + 4x + 4 = (x + 2)^2
To simplify this expression, we can use the fact that (a + b)^2 = a^2 + 2ab + b^2:
(x + 2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4
Therefore, the perfect square trinomial x^2 + 4x + 4 is equivalent to (x + 2)^2.
Explanation: