Question:
Expand:
(i) $(a+2 b+5 c)^{2}$
(ii) $(2 b-b+c)^{2}$
(iii) $(a-2 b-3 c)^{2}$
Solution:
(i) $(a+2 b+5 c)^{2}=(a)^{2}+(2 b)^{2}+(5 c)^{2}+2(a)(2 b)+2(2 b)(5 c)+2(5 c)(a)$
$=a^{2}+4 b^{2}+25 c^{2}+4 a b+20 b c+10 a c$
(ii) $(2 a-b+c)^{2}=[(2 a)+(-b)+(c)]^{2}$
$=(2 a)^{2}+(-b)^{2}+(c)^{2}+2(2 a)(-b)+2(-b)(c)+4(a)(c)$
$=4 a^{2}+b^{2}+c^{2}-4 a b-2 b c+4 a c$
(iii) $(a-2 b-3 c)^{2}=[a+(-2 b)+(-3 c)]^{2}$
$=(a)^{2}+(-2 b)^{2}+(-3 c)^{2}+2(a)(-2 b)+2(-2 b)(-3 c)+2(a)(-3 c)$
$=a^{2}+4 b^{2}+9 c^{2}-4 a b+12 b c-6 a c$
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