%5E2-as-a-trinomial.jpeg "(x-5)^2 As A Trinomial")
Expanding (x-5)^2 as a Trinomial
In algebra, expanding a binomial expression such as (x-5)^2 into a trinomial can be a useful skill to have. In this article, we will explore how to expand (x-5)^2 and understand the resulting trinomial expression.
What is a Binomial?
A binomial is an algebraic expression consisting of two terms, such as x-5. In this case, x and -5 are the two terms.
What is a Trinomial?
A trinomial is an algebraic expression consisting of three terms, such as x^2 - 10x + 25. In this case, x^2, -10x, and 25 are the three terms.
Expanding (x-5)^2
To expand (x-5)^2, we need to follow the binomial theorem, which states that:
(a-b)^2 = a^2 - 2ab + b^2
In our case, a = x and b = 5. Substituting these values into the theorem, we get:
(x-5)^2 = x^2 - 2(x)(5) + 5^2 = x^2 - 10x + 25
The Resulting Trinomial
As we can see, the expansion of (x-5)^2 results in a trinomial expression:
x^2 - 10x + 25
This trinomial expression consists of three terms: x^2, -10x, and 25. Each term has a specific coefficient and variable.
Conclusion
In conclusion, expanding (x-5)^2 as a trinomial involves applying the binomial theorem and substituting the values of a and b. The resulting trinomial expression is x^2 - 10x + 25, which consists of three terms. This skill is essential in algebra and can be applied to various mathematical problems.
