if a=3+b then what is the value of a³-b³-9ab
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Given,
a = 3 + b
⇒ a - b = 3 -------------------------------------(i)
Take cube to both side of the eqation
⇒ (a - b)³ = 3³ = 27
⇒ a³ - b³ - 3ab(a - b) = 27
⇒ a³ - b³ - 3ab(3) = 27 ∵a-b = 3
⇒ a³ - b³ - 9ab = 27
a = 3 + b
⇒ a - b = 3 -------------------------------------(i)
Take cube to both side of the eqation
⇒ (a - b)³ = 3³ = 27
⇒ a³ - b³ - 3ab(a - b) = 27
⇒ a³ - b³ - 3ab(3) = 27 ∵a-b = 3
⇒ a³ - b³ - 9ab = 27
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