Which of the following expression are exactly equal to $4 x^{2} - 4 x y + y^{2}$ in value?

{(2 x - y)}^{2}

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{(3 x - y)}^{2} - (5 x^{2} - 2 x y)

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{(2 x + y)}^{2} - 2 x y

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{(2 x + 3 y)}^{2} - 8 y (2 x + y)

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Solution

The correct options are
A ${(2 x - y)}^{2}$
B ${(3 x - y)}^{2} - (5 x^{2} - 2 x y)$
D ${(2 x + 3 y)}^{2} - 8 y (2 x + y)$
$(A) (2 x - y)^{2} = 4 x^{2} - 4 x y + y^{2}$
$(B) (3 x - y)^{2} - (5 x^{2} - 2 x y) = 9 x^{2} - 6 x y + y^{2} - 5 x^{2} + 2 x y = 4 x^{2} - 4 x y + y^{2}$
$(C) (2 x + y)^{2} - 2 x y = 4 x^{2} + 4 x y + y^{2} - 2 x y = 4 x^{2} + 2 x y + y^{2}$
$(D) (2 x + 3 y)^{2} - 8 y (2 x + y) = 4 x^{2} + 12 x y + 9 y^{2} - 16 x y - 8 y^{2} = 4 x^{2} - 4 x y + y^{2}$
As per following expression the expression (A) ,(B) and (D) are exactly equal to $4 x^{2} - 4 x y + y^{2}$

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Similar questions

1. {(3 x - y)}^{2} - ({5 x}^{2} - 2 x y)

2. {(2 x - y)}^{2}

3. {(2 x + y)}^{2} - 2 x y

4. {(2 x + 3 y)}^{2} - 8 y (2 x + y)

4 x^{2} - 4 x y + y^{2}

(2 x + y - 5)^{2}

8 x^{3} + y^{3}

x - y + 2 z)^{2}

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