Question

Algebraic chapter

Expand the following:

(x - y)2 - (x + y)2​

Answer 1

Question :-

Expand the following :-

$\sf (x - y)^2 - (x + y)^2$

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Answer :-

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Identity used :-

• $\sf (a+b)^2 = a^2 + b^2 + 2ab$
• $\sf (a - b)^2 = a^2 + b^2 - 2ab$

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Solution :-

$\sf = (x - y)^2 - (x + y)^2$

$\sf = x^2 + y^2 - 2xy - [ x^2 + y^2 + 2xy]$

$\sf = x^2 + y^2 - 2xy - x^2 - y^2 - 2xy$

$\sf = \cancel{x^2} + \cancel{y^2} - 2xy - \cancel{x^2 } - \cancel{y^2} - 2xy$

$\sf = -2xy - 2xy$

$\sf = -4xy$

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$\boxed{\sf (x - y)^2 - (x + y)^2 = -4xy}$

Answer 2

Answer:

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Solution :-

$\sf = (x - y)^2 - (x + y)^2=(x−y)$

$\sf = x^2 + y^2 - 2xy - [ x^2 + y^2 + 2xy]=x$

$\sf = x^2 + y^2 - 2xy - x^2 - y^2 - 2xy=x$

$\sf = \cancel{x^2} + \cancel{y^2} - 2xy - \cancel{x^2 } - \cancel{y^2}$

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$\boxed{\sf (x - y)^2 - (x + y)^2 = -4xy}$