I don't really understand this at the moment and haven't got the time to get my head into it so I'll have to come back to it and the other factorising questions you set on the other post in a few days. I'll message you when I've done them rather than you having to check. Thanks for the challenges.

The hyperlink is a lot more elegant than having to have the whole web address in your post, glad it worked for you.

1) 5x(x+3)-2(x+3)

= (x+3)(5x-2)   I guess this is my answer. Not that familiar with this, seemed a bit too simple so worked it the other way to check as usual. Expanded the brackets;

= 5x²-2x+15x-6   Then combined like terms;

= 5x²+13x-6      Then tried to factorise this, looking for something that would multiply to make -30 and add to make 13;

= 5x²-2x+15x-6   Continued factorising and got back to your original question so should be good.

2) -7x(2x-1)-(2x-1)

= (2x-1)(-7x-1)   I think this is my answer. Threw me a bit only having the - in front of the second bracket with no number, but went through the same process and it seems to work ok. Expanded;

= -14x²-2x+7x+1   Combined like terms;

= -14x²+5x+1   Factorise, look for something that multiplies to -14 and adds to 5.

= -14x²+7x-2x+1   Then back to where we started again.

I am quite slow on these. I think I used to just struggle playing around with numbers in brackets until it worked but this is a more deliberate method. 

I am a bit thrown by your hint "HINT:    factorise  5xy-2y     Can you see the similarity?" Was this to relate to question 1?

Yes, unsolvable for x as it is, I was hoping for more information if they replied.

(3x+5)(3x-5)   If I expand this I get;

3x²-15x+15x-25

3x²-25      How you have got to your answer, I have no idea.

I have heard the term "difference of two squares" but that's my only exposure to it.

Thanks Melody, that's quite useful.

There are a number of ways you could do this.

If you know what $${\frac{{\mathtt{2}}}{{\mathtt{5}}}}$$ is as a decimal you could just type this in after the "1", then multiply by "5". I you wanted to know what $${\frac{{\mathtt{2}}}{{\mathtt{5}}}}$$ is as a decimal you could just type 2/5= into a calculator and it would tell you. You might be able to guess this as it's quite a simple fraction.

A possibly quicker method if you didn't know what the decimal of the fraction was would be to type (1+(2/5))*5=   This might look a bit over complicated but it's basically saying 1 and $${\frac{{\mathtt{2}}}{{\mathtt{5}}}}$$ multiplied by 5 equals.

Forgot about the hyperlink.

Just click the chain symbol in the tool bar (though you could also say it looks like a head on view of a pair of glasses at 45 degrees), just under the background colour selector. I'm sure you know or can guess the rest but just in case, the "URL" is the address from the address bar and "Text to display" is where you put "Click here" or whatever text you want to appear as your hyperlink in your post. Sorry if that was teaching you to suck eggs (not sure if that's a term common in your neck of the woods)(oops, there's another one).

Yeh, substituting. Before I knew enough to be able to do this sort of thing as close to properly as I do, I used to just play around with substitution as it was the only way I could work out how to do it with common sense alone. Sometimes it could take a while. For years I developed my own common sense coping strategies for maths as I didn't know the correct methods. I very much doubt I came up with anything new but I did come up with them myself, they were never very quick though. You may see that I do some things a little bit unconventionally.

3x²+36=24x    Subtract 24x from both sides;

3x²-24x+36=0    Not sure if I needed to put the "-24x" in this position but it normally sits here as B in the formula so thought it best? Then I factorised;

3(x²-8x+12)=0    Then I divided both sides by 3 which seemed correct for the left hand side but seemed like a bit of a cheat for the right hand side as $${\frac{{\mathtt{0}}}{{\mathtt{3}}}}$$ stays as 0, but it seems to work;

x²-8x+12=0   Then I factorised again;

(x-6)(x-2)=0   So x=6 or x=2

I have expanded the brackets and substituted the numbers and all seems to check ok. This really does help to make sense of factorising, it gives it a purpose.

I'm still never satisfied though to come up with an answer of it could be this or it could be that, I've always been used to there only really being one correct answer in maths, different ways of getting there but only one correct answer.

There are no like terms that we can combine here so there isn't any more we can do. That is unless you need to solve for "q"? If so we would need to see this followed by an equals sign and what it is equal to.

All you have to do is enter the numbers, decimal points and multiplication and equals signs exactly as you have in your question. This could be on you own calculator or the one provided on the home page.

what is three quarters times three eighths

$${\frac{{\mathtt{3}}}{{\mathtt{4}}}}$$ * $${\frac{{\mathtt{3}}}{{\mathtt{8}}}}$$ = 

This is effectively the same as;

$${\frac{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}\right)}{\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{8}}\right)}}$$ =

Hopefully this helps you to answer your own question, if not please ask for more help.