Verify identity

a3
+b3
=(a+b)(a2
-ab+b2
)


Please answer in LHS = RHS format​

1 thought on “Verify identity<br /><br />a3<br /> +b3<br /> =(a+b)(a2<br /> -ab+b2<br /> )<br /><br /><br />Please answer in LHS = RHS format​”

1. Question :-

   To verify the identity a³+b³ = (a+b)(a² – ab + b²)

   Answer :-

   In order to verify the identity let

   • a = 4
   • b = 1

   By substituting the values,

   ⇒4³ +1³ = (4+1)[4² – (4)(1) + 1²]

   Solving LHS (left hand side of the equation) and RHS (Right hand side of the equation) separately,

   LHS :-

   4³ + 1³

   ⇒ 64 + 1

   ⇒ 65

   RHS :-

   (4+1)[4² – (4)(1) + 1²]

   ⇒ (5)[16 – 4 + 1]

   ⇒ (5)(13)

   ⇒ 65

   LHS = RHS

   Therefore verified

   Some more formulas :-

   • (a+b)² = a² + 2ab + b²
   • (a-b)² = a² – 2ab + b²
   • (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca
   • (x+a)(x+b) = x² + x(a+b) + ab
   • a²-b² = (a+b)(a-b)
   • (a+b)³ = a³ + 3a²b + 3ab² + b³
   • (a-b)³ = a³ – 3a²b + 3ab² – b³
   • a³+b³ = (a+b)(a² – ab + b²)
   • a³-b³ = (a-b)(a² + ab + b²)
   • a³+b³+c³ – 3abc = (a+b+c)(a² + b² + c² – ab – bc – ca)

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