Ask a New Question
Menu

A, (2x^2+6x+1) - (3x^2+3x+9)=-5x^2+3x-8

B, (2x^2+6x+1) -(3x^2+3x+9)= x^2+3x+8

C, (2x^2+6x+1) - (3x^2+3x+9)= -x^2+3x-8

D, (2x^2+6x+1) - (3x^2+3x+9)= 5x^2+9x+10

1 answer

Let's simplify the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

Starting with the expression:

\[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \]

We can distribute the minus sign across the second polynomial:

\[ = 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]

Now, combine like terms:

  1. For the \(x^2\) terms: \[ 2x^2 - 3x^2 = -x^2 \]

  2. For the \(x\) terms: \[ 6x - 3x = 3x \]

  3. For the constant terms: \[ 1 - 9 = -8 \]

Putting it all together, we have:

\[ -x^2 + 3x - 8 \]

Now, we can match this result to the options given:

  • A: \(-5x^2 + 3x - 8\) (not correct)
  • B: \(x^2 + 3x + 8\) (not correct)
  • C: \(-x^2 + 3x - 8\) (correct)
  • D: \(5x^2 + 9x + 10\) (not correct)

The correct answer is C: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).