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2. Polynomials
medium
અવયવ પાડો :
$2 \sqrt{2} a^{3}+8 b^{3}-27 c^{3}+18 \sqrt{2} a b c$
Option A
Option B
Option C
Option D
Solution
We have,
$2 \sqrt{2} a^{3}+8 b^{3}-27 c^{3}+18 \sqrt{2} a b c$
$=\left\{(\sqrt{2} a)^{3}+(2 b)^{3}+(-3 c)^{3}-3(\sqrt{2} a)(2 b)(-3 c)\right\}$
$=\{\sqrt{2} a+2 b+(-3 c)\}\left\{(\sqrt{2} a)^{2}+(2 b)^{2}+(-3 c)^{2}-(\sqrt{2} a)(2 b)-(2 b)(-3 c)-(-3 c)(\sqrt{2} a)\right\}$
$=(\sqrt{2} a+2 b-3 c)\left(2 a^{2}+4 b^{2}+9 c^{2}-2 \sqrt{2} a b+6 b c+3 \sqrt{2} c a\right)$
Standard 9
Mathematics
