a+3b=6 , find the value of a^3+8b^3+27c^3-216
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Step-by-step explanation:
Let us directly substitute a=2b+6 in the expression a
3
−8b
3
−36ab−216 as shown below:
(2b+6)
3
−8b
3
−36b(2b+6)−216
=[(2b)
3
+6
3
+(3×(2b)
2
×6)+(3×2b×6
2
)]−8b
3
−72b
2
−216b−216
(∵(x+y)
3
=x
3
+y
3
+3x
2
y+3xy
2
)
=8b
3
+216+72b
2
+216b−8b
3
−72b
2
−216b−216
=(8b
3
−8b
3
)+(72b
2
−72b
2
)+(216b−216b)+(216−216)
=0
Hence, a
3
−8b
3
−36ab−216=0 when a=2b+6.
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