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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 \( a^3 + b^3 \)

If you have any issues in the \( a^3 + b^3 \) formulas, please let me know through social media and mail. A cube Plus B Cube is most important algebra maths formulas for class 6 to 12.

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