A perfect square trinomial is formed by squaring a binomial. The general forms are:

1. $(a + b)^2 = a^2 + 2ab + b^2$
2. $(a - b)^2 = a^2 - 2ab + b^2$

Two examples:

1. $(3x + 4)^2 = 9x^2 + 24x + 16$
   Explanation: The first term is $(3x)^2 = 9x^2$, the second term is $2(3x)(4) = 24x$, and the last term is $4^2 = 16$.

2. $(2x - 5)^2 = 4x^2 - 20x + 25$
   Explanation: The first term is $(2x)^2 = 4x^2$, the second term is $2(2x)(-5) = -20x$, and the last term is $(-5)^2 = 25$.

Would you like more details on any step?

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Here are five questions to expand on the topic:

1. What is the process for factoring a perfect square trinomial?
2. How do you recognize if a trinomial is a perfect square?
3. Can perfect square trinomials always be factored?
4. What role do coefficients play in identifying perfect square trinomials?
5. How do you apply perfect square trinomials in solving quadratic equations?

Tip: Always check if the middle term is twice the product of the square roots of the first and last terms to confirm a perfect square trinomial.