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