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

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2. Polynomials

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

Option A

Option B

Option C

Option D

Solution

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

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

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

$=4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 z x$

Standard 9

Mathematics

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