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Four of the following five parts numbered (1), (2), (3), (4) and (5) are equal. That one part which is not equal to other four parts is the answer.
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A) \( \Large (2x + 3y)^{2} = \) |
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B) \( \Large (2y - x)^{2} + y (16x + 5y) = \) |
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C) \( \Large 4x (x + 2y) + y (4x + 9y) = \) |
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D) \( \Large (2x + 2y)^{2} + y (4x + 5y) = \) |
Correct Answer:
| B) \( \Large (2y - x)^{2} + y (16x + 5y) = \) |
Description for Correct answer:
(1) \( \Large (2x + 3y)^{2} = 4x^{2} + 9y^{2} + 12xy \)
(2) \( \Large (2y - x)^{2} + y (16x + 5y) \)
= \( \Large 4y^{2} + x^{2} - 4xy + 16xy + 5y^{2} \)
= \( \Large x^{2} + 9y^{2} + 12xy \)
(3) 4x (x + 2y) + y (4x + 9y)
= \( \Large 4x^{2} + 8xy + 4xy + 9y^{2} \)
= \( \Large 4x^{2} + 9y^{2} + 12xy \)
(4) \( \Large (2x + 2y)^{2} - y (4x + 5y) \)
= \( \Large 4x^{2} + 4y^{2} + 8xy + 4xy + 5y^{2} \)
= \( \Large 4x^{2} + 9y^{2} + 12xy \)
(5) \( \Large (2x - y)^{2} + 8y (2x + y) \)
= \( \Large 4x^{2} + y^{2} - 4xy + 16 xy + 8y^{2} \)
= \( \Large 4x^{2} + 9y^{2} + 12xy \)
Thus, we see that except (2), other four expressions are equal
(1) \( \Large (2x + 3y)^{2} = 4x^{2} + 9y^{2} + 12xy \)
(2) \( \Large (2y - x)^{2} + y (16x + 5y) \)
= \( \Large 4y^{2} + x^{2} - 4xy + 16xy + 5y^{2} \)
= \( \Large x^{2} + 9y^{2} + 12xy \)
(3) 4x (x + 2y) + y (4x + 9y)
= \( \Large 4x^{2} + 8xy + 4xy + 9y^{2} \)
= \( \Large 4x^{2} + 9y^{2} + 12xy \)
(4) \( \Large (2x + 2y)^{2} - y (4x + 5y) \)
= \( \Large 4x^{2} + 4y^{2} + 8xy + 4xy + 5y^{2} \)
= \( \Large 4x^{2} + 9y^{2} + 12xy \)
(5) \( \Large (2x - y)^{2} + 8y (2x + y) \)
= \( \Large 4x^{2} + y^{2} - 4xy + 16 xy + 8y^{2} \)
= \( \Large 4x^{2} + 9y^{2} + 12xy \)
Thus, we see that except (2), other four expressions are equal
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