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Question
Factorize each of the following expression:
49(a − b)2 − 25(a + b)2
Solution
\[49(a - b )^2 - 25(a + b )^2 \]
\[ = [7(a - b) ]^2 - [5(a + b) ]^2 \]
\[ = [7(a - b) - 5(a + b)][7(a - b) + 5(a + b)]\]
\[ = (7a - 7b - 5a - 5b)(7a - 7b + 5a + 5b)\]
\[ = (2a - 12b)(12a - 2b)\]
\[ = 2(a - 6b)2(6a - b)\]
\[ = 4(a - 6b)(6a - b)\]
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