%5E2.jpeg "(2m+1)^2")
Expanding (2m + 1)^2
The expression (2m + 1)^2 represents the square of a binomial, which is a polynomial with two terms. To expand this expression, we can use the following methods:
1. Using the FOIL Method
The FOIL method stands for First, Outer, Inner, Last and helps us expand the product of two binomials.
Let's apply it to (2m + 1)^2:
- First: 2m * 2m = 4m^2
- Outer: 2m * 1 = 2m
- Inner: 1 * 2m = 2m
- Last: 1 * 1 = 1
Adding all these terms together: 4m^2 + 2m + 2m + 1 = 4m^2 + 4m + 1
2. Using the Square of a Binomial Formula
The square of a binomial formula states: (a + b)^2 = a^2 + 2ab + b^2
Applying this formula to (2m + 1)^2, we have:
- a = 2m
- b = 1
Therefore: (2m + 1)^2 = (2m)^2 + 2(2m)(1) + 1^2 = 4m^2 + 4m + 1
Summary
Both methods lead to the same expanded form: 4m^2 + 4m + 1.
This expression represents a trinomial (a polynomial with three terms) and is a perfect square trinomial because it can be factored back into (2m + 1)^2.
Understanding how to expand expressions like (2m + 1)^2 is crucial in algebra, especially when simplifying and solving equations.