Question

Question
Consider the polynomial expression
.
Which expression is equivalent to the given polynomial?
Responses ( 2x*2 - 4 )(x+y)-(2 + x)

Answer 1

To simplify the expression \((2x^2 - 4)(x + y) - (2 + x)\), follow these steps:

1. **Distribute** \((2x^2 - 4)\) into \((x + y)\):
\[
(2x^2 - 4)(x + y) = 2x^2 \cdot x + 2x^2 \cdot y - 4 \cdot x - 4 \cdot y
\]
This simplifies to:
\[
2x^3 + 2x^2y - 4x - 4y
\]

2. **Subtract** \((2 + x)\) from the result:
\[
2x^3 + 2x^2y - 4x - 4y - (2 + x)
\]
Distributing the negative sign gives:
\[
2x^3 + 2x^2y - 4x - 4y - 2 - x
\]

3. **Combine like terms**:
\[
2x^3 + 2x^2y - 4x - x - 4y - 2
\]
Combining the \(x\) terms:
\[
2x^3 + 2x^2y - 5x - 4y - 2
\]

Thus, the expression equivalent to the given polynomial is:
\[
2x^3 + 2x^2y - 5x - 4y - 2
\]