SSC CGL 20 Aug 2021 Shift 1 Paper

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Question : 66 of 100

Marks: +1, -0

Simplify

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

.

$4 x z-4 y z$
$2 x z+2 y z$
$4 y z-4 x z$
$4 x z+4 y z$

Solution:

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

=[x+(-y)+z]^{2}-[x+(-y)+(-z)]^{2}

We know that,

(a+b+c)^{2}

=a^{2}+b^{2}+c^{2}+2(a b+b c+c a)

=[(x)^{2}+(-y)^{2}+(z)^{2}+2

\{x ×-y+(-y × z)+z × x\}]

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

\{x ×(-y)+(-y)(-z)+(-z)(x)]

=[x^{2}+y^{2}+z^{2}-2 x y-2 y z

+2 z x-x^{2}-y^{2}-z^{2}+2 x y-2 y z+2 x z]

=[-2 y z+2 z x-2 y z+2 z x]

=4 z x-4 y z

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