Question

Which of the following does not simplify to 12x² - 8x + 15? (Check ALL that apply.)

a) (13x² - 6x + 21) - (x² + 2x + 6)
b) (5x² - 6x + 9) + (7x² + 2x + 6)
c) 2(6x² - 3x + 4) - 2x + 7
d) (16x² + 5x + 10) - (4x² + 13x + 5)

Answer 1

The expressions that do not simplify to 12x² - 8x + 15 are (5x² - 6x + 9) + (7x² + 2x + 6) and 2(6x² - 3x + 4) - 2x + 7.

Step-by-step explanation:

To determine which of the given expressions does not simplify to 12x² - 8x + 15, we can substitute a value for x into each expression and simplify the result. If the expression simplifies to 12x² - 8x + 15, then it is not the correct answer. If the expression gives a different result, then it is a possible answer.

1. (13x² - 6x + 21) - (x² + 2x + 6) = 12x² - 8x + 15. This expression simplifies to 12x² - 8x + 15, so it is not the correct answer.
2. (5x² - 6x + 9) + (7x² + 2x + 6) = 12x² - 4x + 15. This expression does not simplify to 12x² - 8x + 15, so it is a possible answer.
3. 2(6x² - 3x + 4) - 2x + 7 = 12x² - 10x + 15. This expression does not simplify to 12x² - 8x + 15, so it is a possible answer.
4. (16x² + 5x + 10) - (4x² + 13x + 5) = 12x² - 8x + 15. This expression simplifies to 12x² - 8x + 15, so it is not the correct answer.

Therefore, the expressions that do not simplify to 12x² - 8x + 15 are (5x² - 6x + 9) + (7x² + 2x + 6) and 2(6x² - 3x + 4) - 2x + 7.