Question

Simplify the expression

(x^2 + 2x + 3)(x^2 – 2x – 2)

Answer 1

simplified: x^4+3x^2-10x-6 

Answer 2

`x^4-3x^2-10x-6`

Explanation:

To simplify this expression we must apply the distributive property

Distributive Property

`(a+b)(c+d)= ac+ad+bc+bd`

Going over some rules

Law of the signs

`(-)(-)=+\\(-)(+)=-\\(+)(+)=+`

Powers

`Ax^b.Cx^d=ACx^((b+d))`

Simplifying

`(x^2+2x+3)(x^2-2x-2)=x^4-2x^3-2x^2+2x^3-4x^2-4x+3x^2-6x-6`

We add similar terms (those that have the same power)

`x^4-2x^3-2x^2+2x^3-4x^2-4x+3x^2-6x-6\\x^4-3x^2-10x-6`