Question 33

(2x-3y)(x+y)

The expression 2x² - xy - 3y² can be factored as (2x-3y)(x+y). This factorization correctly expands back to the original expression when multiplied.

A) (2x+3y)(x-y)

This option is incorrect because when expanded, (2x+3y)(x-y) yields 2x² - 2xy + 3xy - 3y², which simplifies to 2x² + xy - 3y², a different expression than the original.

B) (x+y)(2x-3y)

This option is also incorrect. When expanded, (x+y)(2x-3y) results in 2x² - 3xy + 2xy - 3y², simplifying to 2x² - xy - 3y², which does not match the original expression.

C) (2x-y)(x+3y)

This option is incorrect as well. Expanding (2x-y)(x+3y) gives 2x² + 6xy - xy - 3y², which simplifies to 2x² + 5xy - 3y², differing from the original expression.

D) (2x-3y)(x+y)

This is the correct option. When expanded, (2x-3y)(x+y) results in 2x² + 2xy - 3xy - 3y², which simplifies to 2x² - xy - 3y², matching the original expression perfectly.

Conclusion

The correct answer, (2x-3y)(x+y), accurately reproduces the original expression upon expansion. All other options fail to reproduce the original expression, either by changing the signs or the coefficients of the terms, demonstrating their incorrectness. Thus, (2x-3y)(x+y) is definitively the right factorization for 2x² - xy - 3y².