Question:
Factorize each of the following algebraic expression:
a2 − 8ab + 16b2 − 25c2
Solution:
$a^{2}-8 a b+16 b^{2}-25 c^{2}$
$=\left(a^{2}-8 a b+16 b^{2}\right)-25 c^{2}$
$=\left[a^{2}-2 \times a \times 4 b+(4 b)^{2}\right]-25 c^{2}$
$=(a-4 b)^{2}-(5 c)^{2}$
$=[(a-4 b)-5 c][(a-4 b)+5 c]$
$=(a-4 b-5 c)(a-4 b+5 c)$
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