simplify (2a-b)³ +(2a-b)³ +12a(4a²-b²)
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Answer:
(2a+b)
3
−(2a−b)
3
Using identity:-
(x+y)
3
=x
3
+y
3
+3x
2
y+3xy
2
(x−y)
3
=x
3
−y
3
−3x
2
y+3xy
2
Therefore,
(2a+b)
3
−(2a−b)
3
=[(2a)
3
+b
3
+3(2a)
2
b+2(2a)b
2
]−[(2a)
3
−b
3
−3(2a)
2
b+2(2a)b
2
]
=[8a
3
+b
3
+12a
2
b+3ab
2
]−[8a
3
−b
3
−12a
2
b+3ab
2
]
=8a
3
+b
3
+12a
2
b+3ab
2
−8a
3
+b
3
+12a
2
b−3ab
2
=b
3
+12a
2
b+b
3
+12a
2
b
=2b
3
+24a
2
b
Hence (2a+b)
3
−(2a−b)
3
=2b
3
+24a
2
b.
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