A minus B Whole Cube
Are you looking for a minus b whole Cube? You can check the formulas of a minus b whole Cube in three ways. We are going to share the (a-b)^3 algebra formulas for you as well as how to create (A-B)^3 and proof.
we can write \( (a-b)^3 = (a-b)^2 \times (a-b) \)
we know that what is the formulas of a minus b whole square. \(a-b)^2 = a^2 +b^2 – 2ab \) put the formulas.
\(=> (a-b)^3 = (a^2+b^2-2ab) \times (a-b)\)
\(=> (a-b)^3 = a \times (a^2+b^2-2ab) – b \times (a^2+b^2-2ab)\)
start multiplication
\(=> (a-b)^3 = a^3 + ab^2 – 2a^2 b – ba^2 – b^3 + 2ab^2 \)
Arrange
\(=> (a-b)^3 = a^3 + ab^2 + 2ab^2 – 2a^2 b – ba^2 – b^3 \)
\(=> (a-b)^3 = a^3 + 3 ab^2 – 3a^2 b – b^3 \)
Also Write : \(=> (a-b)^3 = a^3 – b^3 + 3 ab (b-a) \)
(A-B)^3 Verifications
Need to verify \((a-b)^3\) formula is right or wrong. put the value of a = 5 and b=3
put the value of a and b in the LHS
\(=> (a-b)^3 = (5-3)^3 \)
\(=> (a-b)^3 = (2)^3 \)
\(=> (a-b)^3 = 8 \)
put the value of a and b in the RHS
\(=> a^3 + 3 ab^2 – 3a^2 b – b^3 \)
\(=> 5^3 + 3 \times 5\times 3^2 – 3\times 5^2\times 3 – 3^3 \)
put value of square and cube \(=> 125 + 3 \times 5\times 9 – 3\times 25\times 3 – 27 \)
start multiplication \(=> 125 + 15\times 9 – 75\times 3 – 27 \)
\(=> 125 + 135 – 225 – 27 \)
addition \(=> 260 – 252 \)
Simplify Calculation \(8\)
Therefore \( LHS = RHS \)
Proof Formulas \( (a-b)^3 = a^3 + 3 ab^2 – 3a^2 b – b^3 \)
Summary (A+B)^3
If you have any issues in the (A-B)^3 formulas, please let me know through social media and mail. A minus B Whole Cube is the most important algebra maths formulas for class 6 to 13.
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