The distributive property says that the following is true:
[tex]a(b + c) = ab + ac[/tex]
In our problem, we will consider the term outside (or [tex]a[/tex] in the first equation) to be [tex](x + 3)[/tex] and we will consider the expression inside the parentheses to be [tex](x^2 - 2x + 4)[/tex]. To use the distributive property, we are going to apply the outside term to all terms within the second expression. This is represented as:
[tex](x + 3)(x^2) - (x + 3)(2x) + (x + 3)(4)[/tex]
We can now use the distributive property again to simplify the new expression:
[tex](x + 3)(x^2 - 2x + 4) = x^3 + 3x^2 - 2x^2 - 6x + 4x + 12 = x^3 + x^2 - 2x + 12[/tex]
The answer is x³ + x² - 2x + 12.
