Factorising ab(x^2y^2) - xy(a^2b^2)

To factorise the given expression, ab(x^2y^2) - xy(a^2b^2), we can follow a step-by-step approach. Let's break down the process into smaller sections.

Step 1: Identify the common factors

The expression ab(x^2y^2) - xy(a^2b^2) has two terms separated by a minus sign. To factorise it, we look for common factors between the two terms. In this case, both terms have a common factor of xy. So, we can rewrite the expression as follows:

xy(ab(x^2y) - a^2b^2)

Step 2: Factorise the remaining terms

Now, we need to focus on factorising the remaining terms within the parentheses. Let's look at each term separately.

Term 1: ab(x^2y)
This term has the common factors of ab. So, we can factorise it as ab(xy).

Term 2: a^2b^2
This term is already in its simplest form, so we cannot factorise it further.

Step 3: Simplify the expression

After factorising the individual terms, we can simplify the expression further by combining the factors. The factorised expression becomes:

xy(ab(xy) - a^2b^2)

Final answer:
The given expression ab(x^2y^2) - xy(a^2b^2) can be factorised as xy(ab(xy) - a^2b^2).

Explanation:
In this factorisation process, we identified the common factors between the two terms, which was xy. Then, we factorised the remaining terms separately. Finally, we simplified the expression by combining the factors. This step-by-step approach helps us break down the expression and find its factorised form.