Expand the following


Expand the following

(i) (4a-b + 2c)2           

(ii) (3a – 5b – c)2

(iii) (-x + 2y-3z)2


(i) $(4 a-b+2 c)^{2}=(4 a)^{2}+(-b)^{2}+(2 c)^{2}+2(4 a)(-b)+2(-b)(2 c)+2(2 c)(4 a)$

[using identity, $\left.(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a\right]$

$=16 a^{2}+b^{2}+4 c^{2}-8 a b-4 b c+16 a c$

(ii) $(3 a-5 b-c)^{2}=(3 a)^{2}+(-5 b)^{2}+(-c)^{2}+2(3 a)(-5 b)+2(-5 b)(-c)+2(-c)(3 a)$

[using identity, $(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a$ ]

$=9 a^{2}+25 b^{2}+c^{2}-30 a b+10 b c-6 a c$

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

[using identity, $(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a$ ]

$=x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 x$

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