Question

find the error cheyenne and nicolas are finding ((2x^2 - x) - (3x + 3x^2 - 2)) is either correct? explain your reasoning.
cheyenne ((2x^2 - x) - (3x + 3x^2 - 2) = (2x^2 - x) + (-3x + 3x^2 - 2) = 5x^2 - 4x - 2)
nicolas ((2x^2 - x) - (3x + 3x^2 - 2) = (2x^2 - x) + (-3x = -x^2 - 4x - 2)
select choice select choice found the additive inverse correctly all terms should have been multiplied by select choice

Explanation:

Step1: Rewrite subtraction as addition

$(2x^2 - x) - (3x + 3x^2 - 2) = (2x^2 - x) + (-3x - 3x^2 + 2)$

Step2: Combine like terms (x² terms)

$2x^2 - 3x^2 = -x^2$

Step3: Combine like terms (x terms)

$-x - 3x = -4x$

Step4: Isolate constant term

$+2$

Step5: Verify Cheyenne's error

Cheyenne did not flip the sign of $3x^2$ and $-2$ when finding the additive inverse, so she incorrectly wrote $+3x^2 - 2$ instead of $-3x^2 + 2$.

Step6: Verify Nicolas's error

Nicolas did not flip the sign of $-2$ when finding the additive inverse, so he incorrectly wrote $-2$ instead of $+2$.

Answer:

Neither Cheyenne nor Nicolas is correct.

• Cheyenne failed to correctly find the additive inverse: she did not change the sign of $3x^2$ and $-2$ inside the second parentheses. The correct additive inverse of $(3x + 3x^2 - 2)$ is $(-3x - 3x^2 + 2)$, not $(-3x + 3x^2 - 2)$.
• Nicolas also failed to correctly find the additive inverse: he did not change the sign of $-2$ inside the second parentheses.

The correct simplification is:
$(2x^2 - x) - (3x + 3x^2 - 2) = -x^2 - 4x + 2$