%5E2-expand.jpeg "(2x+5)^2 Expand")
(2x+5)^2: Expansion and Simplification
In algebra, expanding and simplifying expressions are essential skills to master. One common expression that students often stumble upon is (2x+5)^2. In this article, we will explore how to expand and simplify this expression.
What does the caret symbol mean?
Before we dive into the expansion, let's quickly review what the caret symbol ^ means. The caret symbol indicates exponentiation, which means raising a number to a power. In this case, (2x+5)^2 means "2x+5 to the power of 2".
Expanding the Expression
To expand (2x+5)^2, we can use the formula for the square of a sum:
(a+b)^2 = a^2 + 2ab + b^2
In our case, a = 2x and b = 5. Plugging these values into the formula, we get:
(2x+5)^2 = (2x)^2 + 2(2x)(5) + 5^2
Simplifying the Expression
Now that we have expanded the expression, let's simplify it:
(2x)^2 = 4x^2
2(2x)(5) = 20x
5^2 = 25
Substituting these values back into the expression, we get:
(2x+5)^2 = 4x^2 + 20x + 25
And that's the final answer!
Conclusion
Expanding and simplifying expressions like (2x+5)^2 can seem daunting at first, but with the right formula and a bit of practice, it becomes a breeze. Remember to use the formula for the square of a sum, and don't be afraid to break down the expression into smaller parts to simplify it. Happy calculating!
