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Question

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)


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