Factorize each of the following algebraic expressions:

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 $[16(2 l-3 m)+12]\}$

$=4(8 l-12 m+3)(2 l-3 m)$

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