(x + y)(2x + y) + (x + 2y)(x – y)

To simplify the given expression, we can use the distributive property of multiplication over addition.

Step 1: Expand the first term (x + y)(2x + y): (x + y)(2x + y) = x(2x + y) + y(2x + y) = 2x^2 + xy + 2xy + y^2 = 2x^2 + 3xy + y^2

Step 2: Expand the second term (x + 2y)(x - y): (x + 2y)(x - y) = x(x - y) + 2y(x - y) = x^2 - xy + 2xy - 2y^2 = x^2 + xy - 2y^2

Step 3: Combine the expanded terms: 2x^2 + 3xy + y^2 + x^2 + xy - 2y^2

Step 4: Simplify the expression by combining like terms: 3x^2 + 4xy - y^2

Therefore, the simplified expression is 3x^2 + 4xy - y^2.

To simplify the given expression, we can use the distributive property of multiplication over addition.

Step 1: Expand the first term (x + y)(2x + y): (x + y)(2x + y) = x(2x + y) + y(2x + y) = 2x^2 + xy + 2xy + y^2 = 2x^2 + 3xy + y^2

Step 2: Expand the second term (x + 2y)(x - y): (x + 2y)(x - y) = x(x - y) + 2y(x - y) = x^2 - xy + 2xy - 2y^2 = x^2 + xy - 2y^2

Step 3: Combine the expanded terms: 2x^2 + 3xy + y^2 + x^2 + xy - 2y^2

Step 4: Simplify the expression by combining like terms: 3x^2 + 4xy - y^2

Therefore, the simplified expression is 3x^2 + 4xy - y^2.