Question : Simplify the given expression. $(x - 2y)(y - 3x) + (x + y)(x - y) + (x - 3y)(2x + y)$
Option 1: $2y(x - 3y)$
Option 2: $2y(x + 3y)$
Option 3: $2x(x - 3y)$
Option 4: $2x(x + 3y)$
Correct Answer: $2y(x - 3y)$
Solution : Given expression, $(x - 2y)(y - 3x) + (x + y)(x - y) + (x - 3y)(2x + y)$ = $xy-3x^2-2y^2+6xy+x^2-y^2+2x^2+xy-6xy-3y^2$ = $2xy-6y^2$ = $2y(x-3y)$ Hence, the correct answer is $2y(x-3y)$
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