Expanded Form
Let's break down the equation (2x - 1)^2 = (x + 1)^2
and see what we can learn from it.
Expanding the Left Side
To expand the left side of the equation, we need to follow the order of operations (PEMDAS):
(2x - 1)^2 = (2x - 1)(2x - 1)
Multiply the two binomials:
(2x - 1)(2x - 1) = 4x^2 - 4x + 1
So, the expanded form of the left side is 4x^2 - 4x + 1
.
Expanding the Right Side
Now, let's expand the right side of the equation:
(x + 1)^2 = (x + 1)(x + 1)
Multiply the two binomials:
(x + 1)(x + 1) = x^2 + 2x + 1
So, the expanded form of the right side is x^2 + 2x + 1
.
Comparing the Two Expressions
Now that we have expanded both sides of the equation, we can compare them:
4x^2 - 4x + 1 = x^2 + 2x + 1
What can we conclude from this equation?