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Proof A Cube Minus B Cube Formula

Are you looking for a Cube minus b Cube Formula? You can check the formulas of a cube minus b Cube in this way. 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 minus 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)]

\(=> a^3 – b^3  = (a-b)((a-b)^2  + 3ab) \) [use the formula of a minus b whole square]

\(=> a^3 – b^3  = (a-b)(a^2 + b^2 -2ab  + 3ab) \)

\(=> a^3 – b^3  = (a-b)(a^2 + b^2  + ab) \)

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=1

put the value of a and b in the LHS

\( => a^3 – b^3  = 2^3 – 1^3 \)

\( => a^3 – b^3  = 8 – 1 = 7 \)

put the value of a and b in the RHS

\(=> (a-b) (a^2+ b^2 + ab) \)

\(=> (2-1) (2^2+ 1^2 + 2 \times 1) \)

\(=> (1) (4+ 1 + 2) \)

\(=> (1) (7)  = 7\)

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 minus B Cube is the most important algebra maths formulas for class 6 to 12.

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