Can someone please show me how to check the work

Here's the work...

Divide and check.

12a^3b^2+4a^4b^5+16 a b^2/4 a b^2

check for the lowest power of a and for b, and factorize accordingly

ab^2(12a + 4a^3b^3 + 16) / (4ab^2) = (12a + 4a^3b^3 + 16)/4

rewrite each numerical member of the denominator in terms of its factors

(3*4*a + 4*1*a^3b^3 + 4^2)/4

factorize by 4

4(3a + a^3b^3 + 4) / 4 = 3a + a^3b^3 + 4

I need to know how to check it from here. Please show all of your work so I can understand how to do it. Thank you!

12a^3b^2+4a^4b^5+16 a b^2/4 a b^2

4ab^2(3a^2 + a^3b^3 + 4)4ab^2

cancel out 4ab^2 on both numerator and denominator

3a^2 + a^3b^3 + 4

your answer has a slight error on the first term. it must be 3a^2 not 3a