Question:
Factorize each of the following algebraic expression:
49 − x2 − y2 + 2xy
Solution:
$49-x^{2}-y^{2}+2 x y$
$=49-\left(\mathrm{x}^{2}-2 \mathrm{xy}+\mathrm{y}^{2}\right)$
$=49-\left(\mathrm{x}^{2}-2 \times \mathrm{x} \times \mathrm{y}+\mathrm{y}^{2}\right)$
$=7^{2}-(\mathrm{x}-\mathrm{y})^{2}$
$=[7-(\mathrm{x}-\mathrm{y})][7+(\mathrm{x}-\mathrm{y})]$
$=(7-\mathrm{x}+\mathrm{y})(7+\mathrm{x}-\mathrm{y})$
$=(\mathrm{x}-\mathrm{y}+7)(\mathrm{y}-\mathrm{x}+7)$
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