%5E2-4y%5E2%2B2.jpeg "(2y+1)^2-4y^2+2")
Simplifying the Expression (2y+1)^2 - 4y^2 + 2
This article will guide you through simplifying the algebraic expression (2y+1)^2 - 4y^2 + 2.
Step 1: Expanding the Square
The first step is to expand the squared term (2y+1)^2. We can do this by using the formula: (a + b)^2 = a^2 + 2ab + b^2
In this case, a = 2y and b = 1. Applying the formula, we get:
(2y+1)^2 = (2y)^2 + 2(2y)(1) + 1^2 = 4y^2 + 4y + 1
Step 2: Combining Like Terms
Now our expression becomes: 4y^2 + 4y + 1 - 4y^2 + 2
Notice that we have two 4y^2 terms with opposite signs. These will cancel out:
4y^2 - 4y^2 = 0
Step 3: Simplifying the Expression
We are left with: 4y + 1 + 2
Combining the constant terms, the final simplified expression is:
**(2y+1)^2 - 4y^2 + 2 = ** 4y + 3
Conclusion
By expanding the square, combining like terms, and simplifying, we have successfully simplified the expression (2y+1)^2 - 4y^2 + 2 to 4y + 3.