2-(x-y)2-answer.jpeg "(x+y)2-(x-y)2 Answer")
Simplifying (x+y)² - (x-y)²
This expression represents the difference of two squares, a common algebraic pattern that simplifies easily. Let's break down the steps:
Understanding the Pattern
The difference of squares pattern states: a² - b² = (a + b)(a - b)
In our expression, (x + y)² and (x - y)² are both perfect squares:
- a = (x + y)
- b = (x - y)
Applying the Pattern
Let's substitute these values into the pattern:
(x + y)² - (x - y)² = [(x + y) + (x - y)][(x + y) - (x - y)]
Simplifying the Expression
Now, we can simplify the terms within the brackets:
- [(x + y) + (x - y)] = 2x
- [(x + y) - (x - y)] = 2y
Therefore, the simplified expression becomes:
2x * 2y = 4xy
Final Answer
The simplified form of (x+y)² - (x-y)² is 4xy.