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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