Question

Factorize 27x^3-y^3-z^3-9xyz

Answer 1

Answer: A³+B³+C³-3ABC

=(A+B+C)(A²+B²+C²-AB-BC-CA)

=(A+B+C){(A+B+C)²-3(AB+BC+CA)

Replace A with 3x→B=y,C=z

(3x)³+y³+z³-3(3x)yz

=27x³+y³+z³+9xyz

=(3x+y+z){(3x+y+z)²-3(3xy+yz+3xz)}

=(3x+y+z){3x+y+z+√3(3xy+yz+3xz)}

{3x+y+z-√3(3xy+yx+3xz)}

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