What is the formula of (a-b)^4?

Math Staff asked 4 months ago

Answer:

\[\ (a-b)^4 = a^4 – 4a^3b + 6a^2b^2 – 4ab^3 + b^4 \]

Explanation:

\[\ (a-b)^4 = (a-b)^2 \times (a-b)^2 \]

\[\ (a-b)^2 = a^2 + b^2 – 2ab \]

\[\ (a-b)^4 = (a^2 + b^2 – 2ab) \times (a^2 + b^2 – 2ab) \]

Multiplication

\[\  (a^2 ) \times (a^2 + b^2 – 2ab) = a^4 + a^2  b^2 – 2a^3 b  \]

\[\  (b^2 ) \times (a^2 + b^2 – 2ab) = b^2 a^2 + b^4 – 2ab^3 \]

\[\  ( – 2ab) \times (a^2 + b^2 – 2ab) =  4a^2b^2 – 2a^3 b – 2ab^3  \]
Put The Value in a Single Row
\[\ (a-b)^4 = a^4 + a^2  b^2 – 2a^3 b + b^2 a^2 + b^4 – 2ab^3 – 2a^3 b – 2ab^3 + 4a^2b^2 \]
Add Similar Value
\[\ (a-b)^4 = a^4 + 6a^2b^2 + b^4 – 4ab^3 – 4a^3 b \]
\[\ (a-b)^4 = a^4 – 4a^3b + 6a^2b^2 – 4ab^3 + b^4 \]