A perfect square trinomial is a quadratic expression that is the result of squaring a binomial. In other words, it takes the form:

$a^2 + 2ab + b^2 \quad \text{or} \quad a^2 - 2ab + b^2$

These trinomials can always be factored into:

$(a + b)^2 \quad \text{or} \quad (a - b)^2$

Examples:

1. $x^2 + 6x + 9$ is a perfect square trinomial because it factors as $(x + 3)^2$.
2. $x^2 - 8x + 16$ is a perfect square trinomial because it factors as $(x - 4)^2$.

General Form:

1. Positive Form: $(a + b)^2 = a^2 + 2ab + b^2$
2. Negative Form: $(a - b)^2 = a^2 - 2ab + b^2$

Identifying a Perfect Square Trinomial:

1. The first and last terms must be perfect squares.
2. The middle term must be twice the product of the square roots of the first and last terms.

Would you like more details or have any questions?

Relative Questions:

1. What is the difference between a perfect square trinomial and a difference of squares?
2. How can we factor a perfect square trinomial when given an expression?
3. What is the process for identifying non-perfect square trinomials?
4. Can you provide real-life applications of perfect square trinomials?
5. What happens when a trinomial is close to but not exactly a perfect square?

Tip:

To quickly check if a trinomial is a perfect square, compare the middle term to twice the product of the square roots of the first and last terms.