Expand and Simplify Cubic Expressions


So a times the big bracket and negative 1 times the big bracket, so if I expand it out it’s going to be a times that whole thing minus 1 times that whole thing, so a times a squared is a cubed, a times a is a squared, a times 1 is a yep and then negative 1 times a squared is negative a squared negative one times positive a is negative a and negative one times positive one is negative one now. Let’s get to the like terms, there’s a lot of a’s but we can’t gather them all together right?

We only need to gather the like terms, so a cubed there’s no other a cube, so we can’t gather them together, a squared we can look we’ve got a squared there and an a squared there and then we’ve got a and we’ve also got an a here and that’s all the like terms isn’t it?

So let’s do the gathering what’s a squared minus a squared can you guys tell me it’s zero a squared minus a squared is zero, so they cancel out and a minus a again they cancel out zero, so we’re only left with a cubed minus one that is the answer, so see how they all cancel out and it’s really nice like that but what I would do the same thing a times a big bracket, one times the big bracket like that.

So expand it out a a squared is a cubed, a times negative a negative a squared, a times 1 is a,
okay 1 times a squared is a squared now 1 times anything is it’s just itself right 1 times 2 is just 2. 1 times 100 is just 100.

So 1 times this is just as it is a squared minus a plus one, gather your like terms now we’ve got a cubed but no other a cubes we’ve got a negative a squared we’ve also got an a squared here we’ve got an a, we’ve got an a, now the good thing is they again cancel out negative a squared plus a squared they’re the same but they just have different signs so cancel out a minus a, cancel out they all cancel out so we just have a cubed plus one left that’s the answer


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