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

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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.

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Answer 1 · 2018-05-22T15:18:11

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

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.