Simplify the following expression: (8x3+3x2−8x+10)−(7+5x2+5x3)

Question

(
8
𝑥
3
+
3
𝑥
2
−
8
𝑥
+
10
)
−
(
7
+
5
𝑥
2
+
5
𝑥
3
)




(1 point)
Responses

13x3 + 8x2 −8x + 17
13
𝑥
3

+

8
𝑥
2

−
8
𝑥

+

17
13x3 + 8x2 −8x + 17
13
𝑥
3

+

8
𝑥
2

−
8
𝑥

+

17

3x3 + 2x2 −8x − 3
3
𝑥
3

+

2
𝑥
2

−
8
𝑥

−

3
3x3 + 2x2 −8x − 3
3
𝑥
3

+

2
𝑥
2

−
8
𝑥

−

3

3x3 − 2x2 −8x + 3
3
𝑥
3

−

2
𝑥
2

−
8
𝑥

+

3
3x3 − 2x2 −8x + 3
3
𝑥
3

−

2
𝑥
2

−
8
𝑥

+

3

13x3 − 8x2 −2x + 3

Answer 1

To simplify the expression \((8x^3 + 3x^2 - 8x + 10) - (7 + 5x^2 + 5x^3)\), we'll follow these steps:

1. Distribute the negative sign to the terms in the second set of parentheses: \[ (8x^3 + 3x^2 - 8x + 10) - 7 - 5x^2 - 5x^3 \]

2. Combine like terms:

   • For \(x^3\) terms: \(8x^3 - 5x^3 = 3x^3\)
   • For \(x^2\) terms: \(3x^2 - 5x^2 = -2x^2\)
   • For \(x\) terms: \(-8x - 5x = -13x\)
   • For constant terms: \(10 - 7 = 3\)

Thus, combining these results, we have: \[ 3x^3 - 2x^2 - 13x + 3 \]

The correct answer is: \(3x^3 - 2x^2 - 13x + 3\).

None of the provided response options match this answer accurately, so please double-check the options or re-evaluate the problem.