(x%2B2y)%2B4y%5E2.jpeg "(x-2y)(x+2y)+4y^2")
Expanding and Simplifying the Expression (x-2y)(x+2y) + 4y^2
This article will explore the expansion and simplification of the algebraic expression (x-2y)(x+2y) + 4y^2.
Recognizing the Pattern
The first part of the expression, (x-2y)(x+2y), follows a familiar pattern: it represents the product of the sum and difference of two terms. This is known as the difference of squares pattern, which can be expressed as:
(a - b)(a + b) = a^2 - b^2
Applying the Pattern
Using this pattern, we can expand the first part of our expression:
(x-2y)(x+2y) = x^2 - (2y)^2 = x^2 - 4y^2
Combining Terms
Now, let's substitute this back into the original expression:
(x-2y)(x+2y) + 4y^2 = x^2 - 4y^2 + 4y^2
Finally, we can simplify by combining like terms:
x^2 - 4y^2 + 4y^2 = x^2
Conclusion
Therefore, the simplified form of the expression (x-2y)(x+2y) + 4y^2 is x^2. This highlights the importance of recognizing and applying algebraic patterns for efficient simplification.