Expand each of following, using suitable identities : (-2 x+5 y-3 z)^{2}

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2. Polynomials

medium

Expand each of the following, using suitable identities : $(-2 x+5 y-3 z)^{2}$

Option A

Option B

Option C

Option D

Solution

$(-2 x+5 y-3 z)^{2}$

Using $(x+y+z)^{2}=x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 z x,$ we have

$(-2 x+5 y-3 z)^{2}=(-2 x)^{2}+(5 y)^{2}+(-3 z)^{2}+2(-2 x)(5 y)+2(5 y)(-3 z)+2(-3 z)(-2 x)$

$\quad=4 x^{2}+25 y^{2}+9 z^{2}+[-20 x y]+[-30 y z]+[12 z x]$

$=4 x^{2}+25 y^{2}+9 z^{2}-20 x y-30 y z+12 z x$

Standard 9

Mathematics

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