(2x%2By)%2B(x%2B2y)(x-y).jpeg "(x+y)(2x+y)+(x+2y)(x-y)")
Expanding and Simplifying the Expression (x+y)(2x+y)+(x+2y)(x-y)
This article will guide you through the process of expanding and simplifying the expression (x+y)(2x+y)+(x+2y)(x-y).
Expanding the Expression
First, we'll use the distributive property (also known as FOIL) to expand each set of parentheses:
(x+y)(2x+y) = x(2x) + x(y) + y(2x) + y(y) = 2x² + xy + 2xy + y²
(x+2y)(x-y) = x(x) + x(-y) + 2y(x) + 2y(-y) = x² - xy + 2xy - 2y²
Combining Like Terms
Now, we can combine the terms we've obtained from each expansion:
2x² + xy + 2xy + y² + x² - xy + 2xy - 2y²
Combining the x² terms, the xy terms, and the y² terms, we get:
(2x² + x²) + (xy + 2xy - xy + 2xy) + (y² - 2y²) = 3x² + 4xy - y²
Simplified Expression
Therefore, the simplified form of the expression (x+y)(2x+y)+(x+2y)(x-y) is 3x² + 4xy - y².
By following these steps, you can successfully expand and simplify similar expressions.