Simplify:-(a^2 b^3 /ab^3)^-3
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Answer:
given expression (a+b)
3
+(a−b)
3
+6a(a
2
−b
2
) can be solved as follows:
(a+b)
3
+(a−b)
3
+6a(a
2
−b
2
)
=a
3
+b
3
+3a
2
b+3ab
2
+a
3
−b
3
−3a
2
b+3ab
2
+6a
3
−6ab
2
(∵(x+y)
3
=x
3
+y
3
+3x
2
y+3xy
2
,(x−y)
3
=x
3
−y
3
−3x
2
y+3xy
2
)
=(a
3
+a
3
+6a
3
)+(b
3
−b
3
)+(3a
2
b−3a
2
b)+(3ab
2
+3ab
2
−6ab
2
)
=8a
3
Hence, (a+b)
3
+(a−b)
3
+6a(a
2
−b
2
)=8a
3
.
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