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Question
Factorize each of the following algebraic expression:
a2 − 2ab + b2 − c2
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Solution
\[a^2 - 2ab + b^2 - c^2 \]
\[ = ( a^2 - 2ab + b^2 ) - c^2 \]
\[ = ( a^2 - 2 \times a \times b + b^2 ) - c^2 \]
\[ = (a - b )^2 - c^2 \]
\[ = [(a - b) - c][(a - b) + c]\]
\[ = (a - b - c)(a - b + c)\]
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