Question
Factorize of the following algebraic expressions:
$16(2 L-3 m)^2-12(3 m-2 L)$
$16(2 L-3 m)^2-12(3 m-2 L)$
✓
Answer
$16(2 L-3 m)^2-12(3 m-2 L)$
$= 16(2 L-3 m)^2+12(2 L-3)[(3 m-2 L)=-(2 L-3 m)]$
$= {[16(2 L-3 m)+12](2 L-3)[\text { taking }(2 L-3) \text { as the common factor }] }$
$= 4[4(2 L-3 m)+3](2 L-3)[\text { taking } 4 \text { as the common factor] }$
$= 4(8 L-12 m+3)(2 L-3 m)$
$= 16(2 L-3 m)^2+12(2 L-3)[(3 m-2 L)=-(2 L-3 m)]$
$= {[16(2 L-3 m)+12](2 L-3)[\text { taking }(2 L-3) \text { as the common factor }] }$
$= 4[4(2 L-3 m)+3](2 L-3)[\text { taking } 4 \text { as the common factor] }$
$= 4(8 L-12 m+3)(2 L-3 m)$
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