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: $2x(x + 3y)$
Answer (1)
18th Jan, 2024
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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