I am confused on how to determine if an equation/expression is a trinomial square. For example c^2(squared)-18c+81. I know that this is a trinomial square but I don't know why. Could someone please help me understand better
it is, because (c-9)^2 = c^2-18c+81
To determine if an equation or expression is a trinomial square, you need to check if it can be factored into the square of a binomial. Here's how you can analyze the given equation/expression c^2 - 18c + 81 to determine if it is a trinomial square:
1. Check the first term: The first term in the given expression is c^2, which is the square of c. Note that in a trinomial square, the first term must be the square of a binomial.
2. Check the last term: The last term in the given expression is 81. In a trinomial square, the last term must also be a perfect square, which means it should be the square of a number.
3. Check the middle term: In a trinomial square, the middle term is twice the product of the square root of the first term and the square root of the last term. In this case, the first term is c^2, and the last term is 81. The square root of c^2 is c, and the square root of 81 is 9. Twice their product is 2c * 9 = 18c.
Since the middle term (-18c) in the given expression matches the expected value (2c * 9 = 18c) based on the factors of the first and last term, we can conclude that the given expression c^2 - 18c + 81 is indeed a trinomial square.
To make it even clearer, we can write the expression as a square of a binomial:
(c - 9)^2 = c^2 - 18c + 81
Therefore, the given expression is the square of the binomial (c - 9), confirming that it is a trinomial square.