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Addition and Subtraction of Algebraic Expression

Which of the ...

Question

Which of the following expressions are exactly equal in value?
$1. {(3 x - y)}^{2} - ({5 x}^{2} - 2 x y)$
$2. {(2 x - y)}^{2}$
$3. {(2 x + y)}^{2} - 2 x y$
$4. {(2 x + 3 y)}^{2} - 8 y (2 x + y)$

1

and

2

only

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1, 2

and

3

only

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2

and

4

only

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1, 2

and

4

only

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Solution

The correct option is D $1, 2$ and $4$ only
${(3 x - y)}^{2} - ({5 x}^{2} - 2 x y)$
$= 9 x^{2} - 6 x y + y^{2} - 5 x^{2} + 2 x y$
$= 4 x^{2} - 4 x y + y^{2}$
${(2 x - y)}^{2} = 4 x^{2} - 4 x y + y^{2}$
${(2 x - y)}^{2} - 2 x y = 4 x^{2} + 4 x y + y^{2} - 2 x y$
$= 4 x^{2} + 2 x y + y^{2}$
${(2 x + 3 y)}^{2} - 8 y (2 x + y) == 4 x^{2} + 12 x y + {9 y}^{2} - 16 x y - 8 y^{2}$
$= 4 x^{2} - 4 x y + y^{2}$

Suggest Corrections

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Which of the following expressions are exactly equal in value?1.(3x−y)2−(5x2−2xy)2.(2x−y)2 3.(2x+y)2−2xy 4.(2x+3y)2−8y(2x+y)

The correct option is D 1,2 and 4 only(3x−y)2−(5x2−2xy)=9x2−6xy+y2−5x2+2xy=4x2−4xy+y2(2x−y)2=4x2−4xy+y2(2x−y)2−2xy=4x2+4xy+y2−2xy=4x2+2xy+y2(2x+3y)2−8y(2x+y)==4x2+12xy+9y2−16xy−8y2=4x2−4xy+y2

Which of the following expressions are exactly equal in value?
$1. {(3 x - y)}^{2} - ({5 x}^{2} - 2 x y)$
$2. {(2 x - y)}^{2}$
$3. {(2 x + y)}^{2} - 2 x y$
$4. {(2 x + 3 y)}^{2} - 8 y (2 x + y)$