Question

Simplify each expression, and then arrange them in increasing order based on the coefficient of n2. Tiles -5(n3 – n2 – 1) + n(n2 – n) (n2 – 1)(n + 2) – n2(n – 3) n2(n – 4) + 5n3 – 6 2n(n2 – 2n – 1) + 3n2

Answer 1

1. 3) n2(n – 4) + 5n3 – 6 n^2= -4
2. 4) 2n(n2 – 2n – 1) + 3n2 n^2= -1
3. 1) -5(n3 – n2 – 1) + n(n2 – n) n^2= 4
4. 2) (n2 – 1)(n + 2) – n2(n – 3) n^2= 5

Explanation:

Answer 2

1- Simplification of the expressions:
-5(n³-n²-1) + n(n²-n)
-5n³ + 5n² + 5 + n³ - n²
-4n³ + 4n² + 5
Coefficient of n² is 4

(n²-1)(n+2) - n²(n-3)
n³ + 2n² - n - 2 - n³ + 3n²
5n² - n - 2
Coefficient of n² is 5

n²(n-4) + 5n³ - 6
n³ - 4n² + 5n³ - 6
6n³ - 4n² + 6
Coefficient of n² is -4

2n(n²-2n-1) + 3n²
2n³ - 4n² - 2n + 3n²
2n³ - n² - 2n
Coefficient of n² is -1

2- Ordering the equations:
Based on the coefficients calculated in step 1, the correct order would be:
6n³ - 4n² + 6
2n³ - n² - 2n
-4n³ + 4n² + 5
5n² - n - 2

Hope this helps :)