PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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Let us derive some deductions on the learnt cubic identities.
Consider the identity \((a + b)^3\) \(=\) \(a^3\) \(+\) \(3a^2b\) \(+\) \(3ab^2\) \(+\) \(b^3\).
Factor out \(3ab\) from the last two terms of RHS.
 
a+b3=a3+b3+3aba+b
 
Retain \(a^3+b^3\) on one side and transform the remaining terms to the other side of the equation.
 
a3+b3=a+b33aba+b
 
Factor out \((a+b)\) from the RHS of the above equation and simplify.
 
a3+b3=(a+b)[a+b23ab]
 
a3+b3=(a+b)[a2+2ab+b23ab]
 
a3+b3=(a+b)(a2ab+b2)
Consider the identity \((a - b)^3\) \(=\) \(a^3\) \(-\) \(3a^2b\) \(+\) \(3ab^2\) \(-\) \(b^3\).
Factor out \(-3ab\) from the last two terms of RHS.
 
ab3=a3b33abab
 
Retain \(a^3-b^3\) on one side and transform the remaining terms to the other side of the equation.
 
a3b3=ab3+3abab
 
Factor out \((a-b)\) from the RHS of the above equation and simplify.
 
a3b3=(ab)[ab2+3ab]
 
a3b3=(ab)[a22ab+b2+3ab]
 
a3b3=(ab)(a2+ab+b2)