The factorization of 12a^3b^2 +18a²b^2 – 12ab^2 is [tex]6 a b^{2}(a+2)(2 a-1)[/tex]
Solution:
Given, expression is [tex]12 a^{3} b^{2}+18 a^{2} b^{2}-12 a b^{2}[/tex]
We have to factorize the given expression completely.
Now, take the expression
[tex]12 a^{3} b^{2}+18 a^{2} b^{2}-12 a b^{2}[/tex]
Taking [tex]b^2[/tex] as common term,
[tex]b^{2}\left(12 a^{3}+18 a^{2}-12 a\right)[/tex]
Taking "a" as common term,
[tex]b^{2}\left(a\left(12 a^{2}+18 a-12\right)\right)[/tex]
Taking "6" as common term,
[tex]b^{2}\left(a\left(6\left(2 a^{2}+3 a-2\right)\right)\right)[/tex]
Splitting "3a" as "4a - a" we get,
[tex]b^{2}\left(a\left(6\left(2 a^{2}+4 a-a-2\right)\right)\right)[/tex]
[tex]\begin{array}{l}{b^{2}(a(6(2 a(a+2)-1(a+2))))} \\\\ {b^{2}(a(6((a+2) \times(2 a-1))))} \\\\ {6 a b^{2}(a+2)(2 a-1)}\end{array}[/tex]
Hence, the factored form of given expression is [tex]6 a b^{2}(a+2)(2 a-1)[/tex]
