help with factorising 3x(squared) + 6xy

[simp75]

help with factorising 3x(squared) + 6xy maths homework due in tommorow
don't understand it please help

[roslyn251254]

Take 3x outside a bracket ... 3x(x + 2y)
(If you multiply out the bracket you get what you started with)

[Old_Geezer]

Aye, you can see both bits have common parts to them. The x to start with. So divide both by x and shove a 'multiply by x' outside of the bracket where it applies to both.

3x^2 + 6xy

x(3x + 6y)

And the 3 is common too. Again divide both by the 3 and put it outside.

3x(x - 2y)

And voila !

[martinjr]

Should that not be 3x(x+2y) not minus??

[Old_Geezer]

Quite possibly. PCs are always slipping typos into my typing when I'm looking the other way. It annoys me much more than it ought. But the method is sound.

[factor-fiction]

But what is x.....?

[jake-the-peg]

I think you're going to confuse people factor this is not an equation so you can't solve it

[factor-fiction]

.. but I just don't get it sir. What's y then?...I thought this was Maths not English.

[Old_Geezer]

x is the number of fish in the barrel. y represents your ability to hit one with your spear.

[factor-fiction]

Thanks O_G.

As a Maths teacher I (and other teachers) found it very difficult to teach this topic.

Going back 40 years or so as a student I lapped all this stuff up and never had any problems factorising, simplifying, solving equations etc.

But when I came to teach it I was faced with students aged 11-16 who just didn't get it at all. They kept coming back to "but what's x?" or "why have you got w when yesterday you used x" and " I just don't get why you're using letters". Only the better students in just the top sets seemed to be able to cope with algebra. For most of the rest it was a mystery.

So I spent ages researching different theories about teaching algebra and tried different approaches. But I have to confess that however it was taught the vast majority still 'didn't get it'.

I've mentioned this before but when I invigilated a Maths GCSE exam there was a question similar to the one above and several students called me over to tell me there was no y button on their calculators.

I just wish I could put my finger on why more students seemed to grasp this 40-60 years ago (my parents also went to grammar school and coped with it) than grasp it nowadays...or maybe things have always been this way and I was just lucky to go to a good school.