Question

What is the difference between the expression (3x+4x)+2x(3x+4x)+2x and the expression 3x+(4x+2x)3x+(4x+2x) ?(1 point) Responses 2x2x 2 x 4x4x 4 x 0 0 3x

Answer 1

Let's simplify both expressions step by step.

**First expression:** \((3x+4x)+2x(3x+4x)+2x\)

1. Simplify \(3x + 4x\):
\[
3x + 4x = 7x
\]
So, the expression becomes:
\[
7x + 2x(7x) + 2x
\]

2. Expand \(2x(7x)\):
\[
2x \cdot 7x = 14x^2
\]
Now, the expression is:
\[
7x + 14x^2 + 2x
\]

3. Combine like terms \(7x + 2x\):
\[
7x + 2x = 9x
\]
Thus, the first expression simplifies to:
\[
14x^2 + 9x
\]

**Second expression:** \(3x+(4x+2x)3x+(4x+2x)\)

1. Simplify \(4x + 2x\):
\[
4x + 2x = 6x
\]
So, the expression becomes:
\[
3x + (6x)(3x) + 6x
\]

2. Expand \((6x)(3x)\):
\[
6x \cdot 3x = 18x^2
\]
Now, the expression is:
\[
3x + 18x^2 + 6x
\]

3. Combine like terms \(3x + 6x\):
\[
3x + 6x = 9x
\]
Thus, the second expression simplifies to:
\[
18x^2 + 9x
\]

### Comparing Both Expressions:
- First expression: \(14x^2 + 9x\)
- Second expression: \(18x^2 + 9x\)

To find the difference:
\[
(14x^2 + 9x) - (18x^2 + 9x) = 14x^2 + 9x - 18x^2 - 9x
\]
The \(9x\) terms cancel out:
\[
14x^2 - 18x^2 = -4x^2
\]

Thus, the difference between the two expressions is:
\[
\boxed{-4x^2}
\]