how to factorise this 20a^2b + 12ab^2?

20a^2b + 12ab^2
=4ab(5a+3b) answer//

20a^2b + 12ab^2
= 4(5a^2b + 3ab^2)
= 4ab(5a + 3b)

20a^(2b) + 12ab²

We can see that the terms have a common factor of 4a. Noting that a^(2b) divided by a, using the laws of indices, gives a^(2b - 1), we can factorise thus

4a(5a^(2b - 1) + 3b²)

When looking for the greatest common factor, break it down into numbers and variables.

What is the greatest common factor of 20 and 12? 4 is the largest number that will go into both evenly.

What are the variables? a and b
What powers of a and b are common to both terms? Both terms contain an a and b to the first power (plain old a and b).

So the greatest common factor of the two terms is 4ab (combine the numbers and the variables). The GCF can be factored out of both terms to give

4ab(5a + 3b). You can check your answer by using the distributive property and making sure you end up where you started.