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Factorise a cube + 27 b cube plus c cube - 18 ABC |
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Answer» We have 27a 3 +B 3 +8c 3 −18abc =(3A) 3 +(b) 3 +(2c) 3 −3(3a)(b)(2c)We KNOW that x 3 +y 3 +z 3 −3xyz=(x+y+z)(x 2 +y 2 +z 2 −xy−yz−zx)Comparing both, we get x=3a,y=b and z=2cThen (3a+b+2c)[(3a) 2 +(b) 2 +(2c) 2 −(3a)(b)−(b)(2c)−(2c)(3a)]=(3a+b+2c)(9a 2 +b 2 +4c 2 −3ab−2bc−6ac) |
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