What is the formula of (a-b)^3?

Math Staff asked 4 months ago

Answer:

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

Explanation:

\[\ (a-b)^3 = (a-b) \times (a-b)^2 \]

\[\ (a-b)^2 = a^2 + b^2 – 2ab \]

\[\ (a-b)^3 = (a – b) \times (a^2 + b^2 – 2ab) \]

Multiplication

\[\  (a ) \times (a^2 + b^2 – 2ab) = a^3 + a  b^2 – 2a^2 b  \]

\[\  (- b ) \times (a^2 + b^2 – 2ab) = – b a^2 – b^3 + 2ab^2 \]

Put The Value in a Single Row
\[\ (a-b)^3 = a^3 + a  b^2 – 2a^2 b – b a^2 – b^3 + 2ab^2 \]
Add Similar Value
\[\ (a-b)^3 = a^3 – b^3 + 3ab^2 – 3a^2 b \]
\[\ (a-b)^3 = a^3 – 3a^2b + 3ab^2 – b^3 \]