Question:
Factorize each of the following algebraic expressions:
16(2l − 3m)2 −12(3m − 2l)
Solution:
$16(2 l-3 m)^{2}-12(3 m-2 l)$
$=16(2 l-3 m)^{2}+12(2 l-3 m) \quad[\because(3 m-2 l)=-(2 l-3 m)]$
$=[16(2 l-3 m)+12](2 l-3 m) \quad[$ Taking $(2 l-3 m)$ as the common factor $]$
$=4[4(2 l-3 m)+3](2 l-3 m) \quad$ Taking 4 as the common factor of $[16(2 l-3 m)+12]\}$
$=4(8 l-12 m+3)(2 l-3 m)$