Q. 84 I3.9( 10 Votes )

# Simplify(a - b) (a2 + b2 + ab) -(a + b) (a2 + b2 - ab)

The given expression is

(a - b) (a2 + b2 + ab) -(a + b) (a2 + b2 - ab)

= (a.a2 + a.b2 + a.ab-b.a2-b.b2-b.ab)-(a.a2 + a.b2-a.ab + b.a2 + b.b2-b.ab)

= a3 + ab2 + a2b-a2b-b3-ab2-a3-ab2 + a2b-a2b-b3 + ab2

= -2b3

Therefore, (a - b) (a2 + b2 + ab) - (a + b) (a2 + b2 - ab) = -2b3
Method 2:
We know that,
(a - b) (a2 + b2 + ab) = a3 - b3 and (a + b) (a2 + b2 - ab) = a3 + b3
Therefore,
(a - b) (a2 + b2 + ab) - (a + b) (a2 + b2 - ab) = a3 - b- (a3 + b) = -2b3

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