Factorise:

Question:

Factorise:
25 − a2 − b2 − 2ab

Solution:

We have:

$25-a^{2}-b^{2}-2 a b=25-\left(a^{2}+b^{2}+2 a b\right)$

$=25-(a+b)^{2}$

$=(5)^{2}-(a+b)^{2}$

$=\{5+(a+b)\}\{5-(a+b)\}$

$=(5+a+b)(5-a-b)$

$\therefore 25-a^{2}-b^{2}-2 a b=(5+a+b)(5-a-b)$

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