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