CBSE Class 9 Answered
Verify x3
+ y3 + z3 - 3xyz = 
(x + y + z)
[(x - y)2 + (y - z)2 + (z - x)2] and
factorise 64x3 - 125y3 - 64z3 + 240 xyz.
(x + y + z)
[(x - y)2 + (y - z)2 + (z - x)2] and
factorise 64x3 - 125y3 - 64z3 + 240 xyz.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
(x + y + z) [ (x - y)2 + (y - z)2
+ (z - x)2]
(x + y + z) (x2 + y2 -
2xy + y2 + z2 - 2yz + z2 + x2 -
2xz)
=
(x + y + z)
(2x2 + 2y2 + 2z2 - 2xy - 2yz - 2xz)
=
2 (x + y + z)
(x2 + y2 + z2 - xy - yz - xz)
= (x + y + z) (x2 + y2 + z2 - xy - yz - xz)
= x3 + y3 + z3 - 3xyz = LHS.
Consider,
64x3 + 125y3 - 64z3 + 240 xyz
= (4x)3 + (5y)3 + (-4z)3 - 3 (4x) (5y) (-4z)
= (4x + 5y - 4z) (16x2 + 25y2 + 16z2 - 20xy + 20yz + 16xz)
Answered by | 04 Jun, 2014, 03:23: PM
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