2(2)^1/2a^3+8b^3-27c^3+18(2)^1/2abc
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Answer:
2
2
a
3
+8b
3
−27c
3
+18
2
abc
\green {=(\sqrt{2}a+2b-3c)(2a^{2}+4b^{2}+9c^{2}-2\sqrt{2}ab+6bc+3\sqrt{2}ca)}=(
2
a+2b−3c)(2a
2
+4b
2
+9c
2
−2
2
ab+6bc+3
2
ca)
Step-by-step explanation:
2\sqrt{2} a^{3} + 8b^{3} - 27c^{3} + 18\sqrt{2}abc2
2
a
3
+8b
3
−27c
3
+18
2
abc
=(\sqrt{2}a)^{3}+(2b)^{3}+(-3c)^{3}-3\times (\sqrt{2}a)(2b)(-3c)}
\pink { x^{3}+y^{3}+z^{3}-3xyz}x
3
+y
3
+z
3
−3xyz
\orange = { (x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-zx)}=(x+y+z)(x
2
+y
2
+z
2
−xy−yz−zx)
= (\sqrt{2}a+2b-3c)[(\sqrt{2}a)^{2}+(2b)^{2}+(-3c)^{2} - (\sqrt{2}a)(2b)-(2b)(-3c)-(-3c)(\sqrt{2}a)]=(
2
a+2b−3c)[(
2
a)
2
+(2b)
2
+(−3c)
2
−(
2
a)(2b)−(2b)(−3c)−(−3c)(
2
a)]
= (\sqrt{2}a+2b-3c)(2a^{2}+4b^{2}+9c^{2}-2\sqrt{2}ab+6bc+3\sqrt{2}ca)=(
2
a+2b−3c)(2a
2
+4b
2
+9c
2
−2
2
ab+6bc+3
2
ca)
Therefore.,
\red { 2\sqrt{2} a^{3} + 8b^{3} - 27c^{3} + 18\sqrt{2}abc}2
2
a
3
+8b
3
−27c
3
+18
2
abc
\green {=(\sqrt{2}a+2b-3c)(2a^{2}+4b^{2}+9c^{2}-2\sqrt{2}ab+6bc+3\sqrt{2}ca)}=(
2
a+2b−3c)(2a
2
+4b
2
+9c
2
−2
2
ab+6bc+3
2
ca)
Step-by-step explanation:
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