write the decimal number 173.178 in the place value table
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Using the identity (a−b)
3
=a
3
−b
3
−3ab(a−b)
It is given that a−b=3 and ab=10, therefore,
(a−b)
3
=a
3
−b
3
−3ab(a−b)
⇒(3)
3
=a
3
−b
3
−(3×10)(3)
⇒27=a
3
−b
3
−(30×3)
⇒27=a
3
−b
3
−90
⇒a
3
−b
3
=27+90
⇒a
3
−b
3
=117
Hence, a
3
−b
3
=117.
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