Expand and Simplify Linear Expressions

Expand and Simplify Linear Expressions


It says to expand and simplify this. So we’ve got two sets of brackets we want to expand it all out.
So here I want to multiply a with the a and also the positive one, and this time I want to multiply, this time it’s negative a in front, isn’t it? So I want to multiply the negative a to the two and negative a by the negative 2a.

So see how we’ve got different signs we’ve got negative and negative and we’ve got these involved, so that’s why I’m asking you to be extra careful okay so let’s do it a times a is a squared and a times one is just a isn’t it so that’s how I expanded the first one now here, negative a times 2 is negative 2a but see here I change the sign to a positive because look negative a times negative 2a, what’s negative negative guys it’s positive isn’t it so that’s why I change it to a positive and

so many students forget to make this into a positive in their exam so many people forget this so every time you get a question like this be extra careful some people just put a negative in front for some reason because they forget so here negative negative makes a positive and then a times 2a is 2a squared okay so that’s what I did.

Now all we need to do guys is gather up our like terms because that’s how we simplify so let’s go to like terms see how a squared and we’ve got a squared here and we’ve got an a and we’ve got a negative 2a they’re common aren’t they so we’ll gather the common parts like this because a plus 2a sorry a squared plus 2a squared is 3a squared and a minus 2a is negative a, hopefully, I don’t have to explain explain too much of the simplifying because we’ve done that in the previous section so basically I’m gathering up my coefficients together right?

So that’s it that’s the answer to question eight so so again multiply your a with your b and your c and here and whenever you have a minus be extra careful minus b times 2a minus b times negative c and then we do c times a and then we also do c times negative three b okay that’s all you need to do so let’s do it one at a time a times b is a b and a times c is ac easy, now negative b times 2a that’s negative 2a b but again see how I cycle that negative b times negative c, negative negative makes a positive so positive b times c which is just bc okay and then again c times a is ca or ac, we usually like to keep it in alphabetical order so put a first ac and then c times negative 3b is negative 3bc, this time it’s positive and negative so we keep a negative not a positive okay and that’s it,

so now we just gather our like terms to simplify, so see how a b we’ve got ab there we’ve got an ab there any more ab? That’s it now here we’ve got an ac and we’ve got also got an ac here and that’s it right and we’ve got a bc and we’ve also got a bc there because that’s 3bc, so I gathered up my like terms okay so let’s go ahead and gather them up by adding or subtracting our coefficients, so ab and minus 2ab that’s going to be minus ab, okay a b minus 2ab is minus ab now ac plus ac is 2ac and bc minus 3bc is minus two bc easy very soon.

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