Simplify the given expression.
(x - 2y)(y - 3x) + (x + y)(x - y) + (x - 3y)(2x + y)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 2y(x - 3y).
(x - 2y)(y - 3x) + (x + y)(x - y) + (x - 3y)(2x + y)
⇒ xy - 3x2 - 2y2 + 6xy + x2 - xy + yx - y2 + 2x2 + xy - 6xy - 3y2
⇒ - 3x2 - 2y2 + 6xy + x2 + 2yx - y2 + 2x2 - 6xy - 3y2
⇒ - 2y2 + 2yx - y2 - 3y2
⇒ 2xy - 6y2
⇒ 2y(x - 3y)