expand y=(x-3)(x+1)(x+3)

Question

alekos · Answer

have you tried to do it?

anonymous · Answer

the answer i got is $$x ^{3}+x ^{2}-9x-9$$

alekos · Answer

yep, that's it. well done

anonymous · Answer

owh okay thank you... how do i factorize it again?

alekos · Answer

so you want to know how to factorise a cubic?

anonymous · Answer

yes :D

alekos · Answer

ok watch carefully.....

start by grouping

x^3 + x^2 - 9x -9

becomes (x^3 + x^2) and (-9x - 9)

1st group becomes x^2(x+1)  and 2nd group -9(x+1)

each term has the same factor x+1 so we can combine the factors

and we get (x^2-9)(x+1)

looking at x^2-9  we need to find two roots that add up to 0 and when multiplied become -9

these are +3 and -3, so we have (x+3)(x-3)(x+1)

so there you go

alekos · Answer

is that clear?

anonymous · Answer

Going through it
:) give me a min, then i'll be done

anonymous · Answer

if we use long division or the synthetic method, it also can be solved right?

alekos · Answer

yes of course, but you need to firstly work out one of the roots