Final answer:
A perfect square trinomial is a quadratic expression that can be written as the square of a binomial. To determine if a trinomial is a perfect square, we need to check if the first and last terms are perfect squares and if the middle term is double the product of the square roots of the first and last terms. In this case, the only perfect square trinomials are a) x²+6x+9 and d) y²-10y+25.
Step-by-step explanation:
A perfect square trinomial is a quadratic expression that can be written as the square of a binomial. To determine if a trinomial is a perfect square, we need to check if the first and last terms are perfect squares and if the middle term is double the product of the square roots of the first and last terms.
Let's analyze each option:
- a) x²+6x+9 - This is a perfect square trinomial because the first term (x²) and the last term (9) are perfect squares, and the middle term (6x) is double the product of the square roots of the first and last terms (2x).
- b) x²+5x+6 - This is not a perfect square trinomial because the middle term (5x) is not double the product of the square roots of the first and last terms.
- c) y²-4y+16 - This is not a perfect square trinomial because the middle term (-4y) is not double the product of the square roots of the first and last terms.
- d) y²-10y+25 - This is a perfect square trinomial because the first term (y²) and the last term (25) are perfect squares, and the middle term (-10y) is double the product of the square roots of the first and last terms (-5y).
- e) 4x²+12x+9 - This is not a perfect square trinomial because the first term (4x²) is not a perfect square.
Therefore, the perfect square trinomials are a) x²+6x+9 and d) y²-10y+25.