Question

Factorize each of the following algebraic expressions:
16(2l − 3m)² −12(3m − 2l)

Answer 1

\[16(2l - 3m )^2 - 12(3m - 2l)\]
\[ = 16(2l - 3m )^2 + 12(2l - 3m) [ \because (3m - 2l) = - (2l - 3m)]\]
\[ = [16(2l - 3m) + 12](2l - 3m) [\text{ Taking }(2l - 3m)\text{ as the common factor }]\]
\[ = 4[4(2l - 3m) + 3](2l - 3m) {\text{ Taking 4 as the common factor of }[16(2l - 3m) + 12]}\]
\[ = 4(8l - 12m + 3)(2l - 3m)\]