Question

(6p^2q^2) - (9pq^3)?

I honestly don't know how to factorise and I really need my homework done for tomorrow, thank you for your help if you may.

Answer 1

`(6p^2q^2) - (9pq^3) = 3pq^2(2p - 3q)`

Explanation:

It helps to use the script function in Socrates - makes it easier to read. I read your expression as `(6p^2q^2) - (9pq^3)`

First, you don't need the parentheses here, since you have only one term in each parenthesis. Therefore you can write it as:

`(6p^2q^2) - (9pq^3) = 6p^2q^2 - 9pq^3`

Next we need to ask: What is common in the two terms?

Firstly: 6 and 9 are both multiples of 3: `6= 2*3` and `9= 3*3`. We can, therefore, draw it out from both terms.

Secondly: `p^2q^2` and `pq^3` both have `p` and `q^2` in common, so we can also draw them out from both terms.

So from the 1st term: `6p^2q^2=3pq^2*2p`
2nd term: `9pq^3=3pq^2*3q`

If we combine these, we get:
`3pq^2*2p - 3pq^2*3q=3pq^2(2p - 3q)` where we put together those parts that are not equal in the two terms.

This gives us:
`(6p^2q^2) - (9pq^3) = 3pq^2(2p - 3q)`

I hope the step by step example was suffiently clear so that you could see what we do.