%5E2-trinomial.jpeg "(x+10)^2 Trinomial")
Expanding (x + 10)^2: A Trinomial Exploration
The expression (x + 10)^2 represents the square of a binomial, which expands into a trinomial. Understanding how to expand this expression is crucial in algebra and has applications in various fields.
Understanding the Concept
The expression (x + 10)^2 signifies multiplying the binomial (x + 10) by itself.
Here's the expansion:
(x + 10)^2 = (x + 10)(x + 10)
Using the FOIL Method
To expand the expression, we can utilize the FOIL method, which stands for First, Outer, Inner, Last. This method helps systematically multiply each term in the first binomial by each term in the second binomial:
First: x * x = x^2
Outer: x * 10 = 10x
Inner: 10 * x = 10x
Last: 10 * 10 = 100
Adding all these products together, we obtain:
(x + 10)^2 = x^2 + 10x + 10x + 100
Simplifying the Trinomial
Combining the like terms (10x and 10x), we get the simplified trinomial:
(x + 10)^2 = x^2 + 20x + 100
The Trinomial's Structure
The expanded trinomial (x^2 + 20x + 100) follows a specific pattern:
- First term: The square of the first term of the binomial (x^2)
- Middle term: Twice the product of the two terms in the binomial (2 * x * 10 = 20x)
- Last term: The square of the second term of the binomial (10^2 = 100)
Generalization
This pattern holds true for any binomial squared:
(a + b)^2 = a^2 + 2ab + b^2
Conclusion
Understanding how to expand (x + 10)^2 into a trinomial using the FOIL method or recognizing the pattern is a fundamental skill in algebra. This knowledge allows for simplifying expressions, solving equations, and tackling more complex mathematical problems.