Proof A Cube Plus B Cube Formula
Are you looking for a Cube plus b Cube Formula? You can check the formulas of a cube plus b Cube in this ways. We are going to share the \( a^3 + b^3 \) algebra formulas for you as well as how to create \( a^3 + b^3 \) and proof.
we know that what is the formulas of \((a+b)^3 \). use the of this formula to prove a cube plus b cube formula.
\(=> (a+b)^3 = a^3 + b^3 + 3ab (a+b) \)
\(=> (a+b)^3 – 3ab (a+b)= a^3 + b^3 \)
\(=> a^3 + b^3 = (a+b)^3 – 3ab (a+b)\) [Note: Take comman part (a+b)]
\(=> a^3 + b^3 = (a+b) ((a+b)^2 – 3ab) \)
we know that formula of \( (a+b)^2 =a^2+ b^2 + 2ab \)
\(=> a^3 + b^3 = (a+b) (a^2+ b^2 + 2ab – 3ab) \)
\(=> a^3 + b^3 = (a+b) (a^2+ b^2 – ab) \)
Proof Formula \(=> a^3 + b^3 = (a+b) (a^2+ b^2 – ab) \)
Verify \( a^3 + b^3 \) Formula
Need to verify \( a^3 + b^3 \) formula is right or wrong. put the value of a =2 and b=3
put the value of a and b in the LHS
\( => a^3 + b^3 = 2^3 + 3^3 \)
\( = > a^3 + b^3 = 8 + 27 = 35 \)
put the value of a and b in the RHS
\(=> (a+b) (a^2+ b^2 – ab) \)
\(=> (2+3) (2^2+ 3^2 -2 \times 3) \)
\(=> (5) (4+ 9 – 6) \)
\(=> (5) (7) = 35 \)
Therefore \( LHS = RHS \) [LHR = left hand side, RHS = right hand side]
Verify Formula \(=> a^3 + b^3 = (a+b) (a^2+ b^2 – ab) \)
Summary \( a^3 + b^3 \)
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