%5E2-simplify.jpeg "(2x-5)^2 Simplify")
Simplifying (2x-5)^2
When working with algebraic expressions, simplifying them is an essential step in solving equations and inequalities. In this article, we will learn how to simplify the expression (2x-5)^2.
What does the caret symbol mean?
Before we dive into simplifying the expression, let's quickly review what the caret symbol (^) means. In mathematics, the caret symbol is used to represent exponentiation. For example, x^2 means "x squared" or "x to the power of 2".
Expanding the expression
To simplify (2x-5)^2, we need to expand the expression using the rule of exponentiation, which states that (a+b)^2 = a^2 + 2ab + b^2. In this case, a = 2x and b = -5.
Using the rule, we can expand the expression as follows:
(2x-5)^2 = (2x)^2 - 2(2x)(5) + (-5)^2
Simplifying the expression
Now, let's simplify each term:
(2x)^2 = 4x^2-2(2x)(5) = -20x(-5)^2 = 25
So, the expanded expression becomes:
(2x-5)^2 = 4x^2 - 20x + 25
And that's it! We have successfully simplified the expression (2x-5)^2.
Conclusion
Simplifying algebraic expressions like (2x-5)^2 is an important skill in mathematics. By using the rule of exponentiation and expanding the expression, we can simplify it to a more manageable form. Remember to always follow the order of operations (PEMDAS) and simplify each term carefully to get the correct answer.
