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 $(2 x + 3 y)^{2} - 8 y (2 x + y)$
$(A)$ $(2 x - y)^{2} = (2 x)^{2} + y^{2} - 2.2 x . y = 4 x^{2} - 4 x y + y^{2}$
$(B)$ $(3 x - y)^{2} - (5 x^{2} - 2 x y) = (3 x)^{2} + y^{2} - 2.3 x . y - 5 x^{2} + 2 x y = 4 x^{2} - 4 x y + y^{2}$
$(C)$ $(2 x + y)^{2} - 2 x y = (2 x)^{2} + y^{2} + 2.2 x . y - 2 x y = 4 x^{2} + 2 x y + y^{2}$
$(D)$ $(2 x + 3 y)^{2} - 8 y (2 x + y) = (2 x)^{2} + (3 y)^{2} + 2.2 x .3 y - 16 x y - 8 y^{2} = 4 x^{2} - 4 x y + y^{2}$
So, $A$ , $B$ , $D$ are correct.

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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)

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

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

x - y + 2 z)^{2}

(2 x - y)^{2} = 4 x^{2} + y^{2} - 4 x y

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