A perfect square trinomial is a trinomial of the form ax^2 + bx + c, where a, b, and c are real numbers and a ≥ 0. The trinomial is a perfect square trinomial if and only if b^2 = 4ac.
To determine if a trinomial is a perfect square trinomial, you can follow these steps:
1. Check if the first and last terms are perfect squares. A perfect square is a number that can be written as the square of another number. For example, 16 is a perfect square because it can be written as 4^2.
2. If the first and last terms are perfect squares, then check if the middle term is twice the product of the square roots of the first and last terms. The square root of a number is a number that, when multiplied by itself, equals the original number. For example, the square root of 16 is 4 because 4 × 4 = 16.
If the middle term is twice the product of the square roots of the first and last terms, then the trinomial is a perfect square trinomial. Otherwise, it is not a perfect square trinomial.
Here are some examples of perfect square trinomials:
* x^2 + 4x + 4
* 9x^2 + 12x + 36
* 16y^2 - 32y + 64
Here are some examples of trinomials that are not perfect square trinomials:
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Answer:
A perfect square trinomial is a trinomial of the form ax^2 + bx + c, where a, b, and c are real numbers and a ≥ 0. The trinomial is a perfect square trinomial if and only if b^2 = 4ac.
To determine if a trinomial is a perfect square trinomial, you can follow these steps:
1. Check if the first and last terms are perfect squares. A perfect square is a number that can be written as the square of another number. For example, 16 is a perfect square because it can be written as 4^2.
2. If the first and last terms are perfect squares, then check if the middle term is twice the product of the square roots of the first and last terms. The square root of a number is a number that, when multiplied by itself, equals the original number. For example, the square root of 16 is 4 because 4 × 4 = 16.
If the middle term is twice the product of the square roots of the first and last terms, then the trinomial is a perfect square trinomial. Otherwise, it is not a perfect square trinomial.
Here are some examples of perfect square trinomials:
* x^2 + 4x + 4
* 9x^2 + 12x + 36
* 16y^2 - 32y + 64
Here are some examples of trinomials that are not perfect square trinomials:
* x^2 + 3x + 2
* 9x^2 + 12x + 8
* 16y^2 - 32y + 40
I hope this helps!