Question

Factorize each of the following algebraic expression:
a² − 2ab + b² − c²

Answer 1

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