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

1 answer

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: \[ \boxed{-4x^2} \]