Question:
Factorize each of the following algebraic expression:
49 − a2 + 8ab − 16b2
Solution:
$49-a^{2}+8 a b-16 b^{2}$
$=49-\left(\mathrm{a}^{2}-8 \mathrm{ab}+16 \mathrm{~b}^{2}\right)$
$=49-\left[\mathrm{a}^{2}-2 \times \mathrm{a} \times 4 \mathrm{~b}+(4 \mathrm{~b})^{2}\right]$
$=7^{2}-(\mathrm{a}-4 \mathrm{~b})^{2}$
$=[7-(\mathrm{a}-4 \mathrm{~b})][7+(\mathrm{a}-4 \mathrm{~b})]$
$=(7-\mathrm{a}+4 \mathrm{~b})(7+\mathrm{a}-4 \mathrm{~b})$
$=-(\mathrm{a}-4 \mathrm{~b}-7)(\mathrm{a}-4 \mathrm{~b}+7)$
$=-(\mathrm{a}-4 \mathrm{~b}+7)(\mathrm{a}-4 \mathrm{~b}-7)$
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