Simplify the expression: (x - y) (3x + xy - 4y) + xy^2 - x^2y
(x - y) (3x + xy - 4y) + xy^2 - x^2y
= (x-y)(3x + xy - 4y) - xy(x - y)
= (x-y)(3x + xy - 4y - xy)
= (x-y)(3x - 4y)
Thank you very much Reiny.
To simplify the expression, let's start by using the distributive property to multiply the two binomials.
Step 1: Multiply the first terms in each binomial:
(x - y) * 3x = 3x^2 - 3xy
Step 2: Multiply the first term in the first binomial with the second term in the second binomial:
(x - y) * xy = xy^2 - xy
Step 3: Multiply the second term in the first binomial with the first term in the second binomial:
(x - y) * (-4y) = -4xy + 4y^2
Step 4: Multiply the second terms in each binomial:
xy^2 - x^2y
Now, let's combine all the terms:
(3x^2 - 3xy) + (xy^2 - xy) + (-4xy + 4y^2) + xy^2 - x^2y
Group similar terms together:
3x^2 + xy^2 - 3xy - xy - 4xy + xy^2 + 4y^2 + xy^2 - x^2y
Combine like terms:
3x^2 - x^2y + 2xy^2 - 6xy + 4y^2
So, the simplified expression is 3x^2 - x^2y + 2xy^2 - 6xy + 4y^2.