Factorise:100 − (x − 5)2
We have:
$100-(x-5)^{2}=(10)^{2}-(x-5)^{2}$
$=\{10+(x-5)\}\{10-(x-5)\}$
$=(10+x-5)(10-x+5)$
$=(5+x)(15-x)$
$\therefore 100-(x-5)^{2}=(5+x)(15-x)$
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