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A. (2x²+6x+1) - (3x²+3x+9) = x²+3x+8

B. (2x²+6x+1) - (3x²+3x+9) = -x²+3x-8
C. (2x²+6x+1) - (3x²+3x+9) = -5x²+9x+10
D. (2x²+6x+1) - (3x²+3x+9) = 5x²+9x+10

1 answer

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

  1. Distribute the negative sign across the second polynomial: \[ (2x^2 + 6x + 1) - 3x^2 - 3x - 9 \]

  2. Combine like terms:

    • For the \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
    • For the \(x\) terms: \(6x - 3x = 3x\)
    • For the constant terms: \(1 - 9 = -8\)

Putting it all together, we have: \[ -x^2 + 3x - 8 \]

Hence, the correct simplified expression is: \[ -x^2 + 3x - 8 \]

Looking at the options provided, the correct answer corresponds to: B. \((2x²+6x+1) - (3x²+3x+9) = -x²+3x-8\).