To simplify the expression 3x(x - y) + y(x - y), we can use the distributive property and combine like terms.
1. Distribute 3x to both terms inside the parentheses:
3x * x = 3x^2
3x * -y = -3xy
2. Distribute y to both terms inside the parentheses:
y * x = xy
y * -y = -y^2
Now, we can combine the like terms:
3x^2 - 3xy + xy - y^2
To combine the terms with x, we add the coefficients:
3x^2 - 2xy - y^2
Therefore, the simplified expression is 3x^2 - 2xy - y^2.