Question
What do we get after factorizing x3+ 8y3+ z3 – 4xyz?
- (x + 2y + z) (x2 + 4y2 + z2 – 2xy – 2yz – zx)
- (x + 2y + z) (x2 + 4y2 + z2 – 2xy – 2yz – zx)
- (x + 2y + z) (x2 + 4y2 + z2 – 2xy – 2yz – zx)
- (x + 2y + z) (x2 + 4y2+ z2 – 2xy – 2yz – zx)
The correct answer is: (x + 2y + z) (x2 + 4y2 + z2 – 2xy – 2yz – zx)
STEP BY STEP SOLUTION
We know that a3 + b3 + c3 – 3abc = (a + b - c) (a2 + b2 + c2 – ab – bc – ca)
In x3 + 8y3 + y3 – 6xyz, a = x, b = 2y and c = z
By using the above equation, we get x3 + 8y3 + z3 – 4xyz = (x+2y+z) (x2 + (2y)2 + z2 – x(2y) – (2y)(z) – zx)
= (x + 2y + z) (x2 + 4y2 + z2 – 2xy – 2yz – zx).
In x3 + 8y3 + y3 – 6xyz, a = x, b = 2y and c = z
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