Final answer:
To find the perfect square trinomial of (a + b)^2, we use the formula a^2 + 2ab + b^2. The perfect square binomial that complements this trinomial is (a + b), as it is the square root of the trinomial.
Step-by-step explanation:
The student is asking about finding the perfect square trinomial that comes from squaring the binomial (a + b) and then identifying the perfect square binomial that complements it. To square the binomial (a + b), we use the formula (a + b)^2 = a^2 + 2ab + b^2, which gives us the perfect square trinomial. The perfect square binomial that complements this trinomial is simply (a + b), which is the square root of the trinomial.
To 'undo' or find the square root of a perfect square trinomial, we take each term and consider the square root of the first and last terms and the root of the middle term divided by 2 for the coefficient of the binomial. For instance, the square root of a^2 is a, and the square root of b^2 is b, while the square root of 2ab, which is the middle term, is ab (because 2ab is the result of 2 * a * b when the binomial (a + b) is squared).