Question

Simplify the following expression:(x+3)-[(x+2)(x³ - 1)]( A. - x^ - 2x3 +2x+5B. --2x³x+2O C. - x4 - 2x + 1OD. -x-2x²+2x+5

Answer 1

Given the expression:

`(x+3)-\lbrack(x+2)(x^3-1)\rbrack`

You can simplify it as follows:

1. Apply the FOIL Method to multiply the binomials inside the square brackets. This method states that:

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

You need to remember the Sign Rules for Multiplication:

`\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ +\cdot-=- \\ -\cdot+=- \end{gathered}`

It is important to remember that, according to the Product of Powers Property, you need to add the exponents when you multiply powers with the same base.

Then, you get:

`=(x+3)-\lbrack(x)(x^3)-(x)(1)+(2)(x^3)-(2)(1)\rbrack`
`=(x+3)-\lbrack x^4-x+2x^3-2\rbrack`

2. Distribute the negative sign:

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

3. Add the like terms:

`=x+3-x^4+x-2x^3+2`
`=-x^4-2x^3+2x+5`

Hence, the answer is: Option A.