1
Question
Factorise :
2√2a³ + 16√2b³ + c³ - 12abc
Factorise :
2√2a³ + 16√2b³ + c³ - 12abc
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Solution
2√2a³+16√2b³+c³-12abc
=(√2a)³+(2√2b)³+c³-12abc May be you need to know the identity
x³+y³+z³+3xyz=
(x+y+z)(x²+y²+z²-xy-zx-yz)
Setting x=a√2,y=b2√2,z=c,we have it equal to
(a√2+b2√2+c)(2a²+8b²+c²-4ab-ac√2-bc2√2)
=(√2a)³+(2√2b)³+c³-12abc
May be you need to know the identity
x³+y³+z³+3xyz=
(x+y+z)(x²+y²+z²-xy-zx-yz)
Setting x=a√2,y=b2√2,z=c,we have it equal to
(a√2+b2√2+c)(2a²+8b²+c²-4ab-ac√2-bc2√2)
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