Question

How do you simplify `(x-3)^3`?

Answer 1

`x^3-9x^2+27x-27`

Explanation:

`"Given " (x+a)(x+b)(x+c)" then expansion is"`

`x^3+(a+b+c)x^2+(ab+bc+ac)x+abc`

`rArr(x-3)^3`

`=(x-3)(x-3)(x-3)`

`"with " a=b=c=-3`

`rArr(x-3)^3`

`=x^3+(-3-3-3)x^2+(9+9+9)x`
`color(white)(xx)+(-3)(-3)-3)`

`=x^3-9x^2+27x-27`

Answer 2

An alternate way to work it using binomial expansion

Explanation:

An alternate way to do this is to use Binomial Expansion, which uses the general formula of:

`(a+b)^n=(C_(n,0))a^nb^0+(C_(n,1))a^(n-1)b^1+...+(C_(n,n))a^0b^n`

So here we have:

• `a=x`
• `b=-3`
• `n=3`

`((C,a,b,"term"),(1,x^3,1,x^3),(3,x^2,-3,-9x^2),(3,x,9,27x),(1,1,-27,-27))`

and we add them up:

`x^3-9x^2+27x-27`