Question

How do you multiply (x-1)(x+1)(x+2)?

Answer 1

`p(x)=x^3+2x^2-x-2`

Explanation:

Let ,

`p(x)=(x-1)(x+1)(x+2)`

Multiplying first two factors:

`p(x)={x(x+1)-1(x+1)}(x+2)`

`p(x)={x*x+x*1-1*x-1*1}(x+2)`

`p(x)={x^2+cancelx-cancelx-1}(x+2)`

`p(x)=(x^2-1)(x+2)`

Again multiplying two factors :

`p(x)=x^2(x+2)-1(x+2)`

`p(x)=x^2*x+x^2*2-1*x-1*2`

`p(x)=x^3+2x^2-x-2`

Answer 2

`x^3+2x^2-x-2`

Explanation:

`"given "(x+a)(x+b)(x+c)`

`"then the expansion is"`

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

`"here "a=-1,b=1,c=2`

`=x^3+(-1+1+2)x^2+(-1+2-2)x`
`color(white)(=)+(-1)(1)(2)`

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