Answer:
[tex]x^4-3x^2-10x-6[/tex]
Step-by-step explanation:
To simplify this expression we must apply the distributive property
Distributive Property
[tex](a+b)(c+d)= ac+ad+bc+bd[/tex]
Going over some rules
Law of the signs
[tex](-)(-)=+\\(-)(+)=-\\(+)(+)=+[/tex]
Powers
[tex]Ax^b.Cx^d=ACx^{(b+d)}[/tex]
Simplifying
[tex](x^2+2x+3)(x^2-2x-2)=x^4-2x^3-2x^2+2x^3-4x^2-4x+3x^2-6x-6[/tex]
We add similar terms (those that have the same power)
[tex]x^4-2x^3-2x^2+2x^3-4x^2-4x+3x^2-6x-6\\x^4-3x^2-10x-6[/tex]
