Simplify (9x2−6x+2)−(x2+4x−39)

Question

Simplify (9x2−6x+2)−(x2+4x−39)
.(1 point)
The difference of the polynomials is

GPT-4o mini · Answer

To simplify the expression $(9x^2 - 6x + 2) - (x^2 + 4x - 39)$, we will first distribute the negative sign to the terms in the second polynomial and then combine like terms. 1. Rewrite the expression: $$ (9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39 $$ 2. Combine like terms: - For the $x^2$ terms: $$ 9x^2 - x^2 = 8x^2 $$ - For the $x$ terms: $$ -6x - 4x = -10x $$ - For the constant terms: $$ 2 + 39 = 41 $$ 3. Putting it all together: $$ 8x^2 - 10x + 41 $$ Thus, the simplified expression is: $$ \boxed{8x^2 - 10x + 41} $$

Answer

Distribute the subtraction (−1), then combine like terms.

GPT-4o mini · Answer

To distribute the subtraction (−1) and combine like terms for the expression $(9x^2 - 6x + 2) - (x^2 + 4x - 39)$, we will follow these steps:

Distribute the negative sign to the second polynomial: \[ (9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - 1 \cdot x^2 - 1 \cdot 4x + 1 \cdot 39 \] This becomes: \[ 9x^2 - 6x + 2 - x^2 - 4x + 39 \]
Combine like terms:
- For the $x^2$ terms: \[ 9x^2 - x^2 = 8x^2 \]
- For the $x$ terms: \[ -6x - 4x = -10x \]
- For the constant terms: \[ 2 + 39 = 41 \]
Putting it all together: \[ 8x^2 - 10x + 41 \]

Thus, the simplified expression is: \[ \boxed{8x^2 - 10x + 41} \]