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Question
Factorize each of the following algebraic expression:
x2 + 2x + 1 − 9y2
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Solution
\[x^2 + 2x + 1 - 9 y^2 \]
\[ = ( x^2 + 2x + 1) - 9 y^2 \]
\[ = ( x^2 + 2 \times x \times 1 + 1) - 9 y^2 \]
\[ = (x + 1 )^2 - (3y )^2 \]
\[ = [(x + 1) - 3y][(x + 1) + 3y]\]
\[ = (x + 1 - 3y)(x + 1 + 3y)\]
\[ = (x + 3y + 1)(x - 3y + 1)\]
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