Question

Simplify each expression, and then arrange them in increasing order based on the coefficient of n^2 .

Answer 1

Increasing order based on coefficient of n^2....

-5(n^3 - n^2 - 1) + n(n^2 - n) <=== this goes in the first box (the top one)
-5n^3 + 5n^2 + 5 + n^3 - 1
-4n^3 + 5n^2 + 4

(n^2 - 1)(n + 2) - n^2(n - 3) <=== this goes in the third box
n^3 + 2n^2 - n - 3 - n^3 + 3n^2
5n^2  - n - 3

n^2(n - 4) + 5n^3 - 6 <=== this goes in the forth box (bottom box)
n^3 - 4n^2 + 5n^3 - 6
6n^3 - 4n^2 - 6

2n(n^2 - 2n - 1) + 3n^2 <=== this goes in second box
2n^3 - 4n^2 - 2n + 3n^2
2n^3 - n^2 - 2n 

Answer 2

Answer:

Step-by-step explanation:

1. The given expression is:

$-5(n^3-n^2-1)+n(n^2-n)$

On simplifying, we get

$-5n^3+5n^2+5+n^3-n^2$

$-4n^3+4n^2+5$

The coefficient of $n^2$ is 4.

2. The given expression is:

$(n^2-1)(n+2)-n^2(n-3)$

On simplifying, we get

$n^3-n+2n^2-2-n^3+3n^2$

$5n^2-n-2$

The coefficient of $n^2$ is 5.

3. The given expression is:

$n^2(n-4)+5n^3-6$

On simplifying, we get

$n^3-4n^2+5n^3-6$

$6n^3-4n^2-6$

The coefficient of $n^2$ is -4.

4. The given expression is:

$2n(n^2-2n-1)+3n^2$

$2n^3-4n^2-2n+3n^2$

$2n^3-n^2-2n$

The coefficient of  $n^2$ is -1.

Now, arranging in the increasing order, we have

$n^2(n-4)+5n^3-6$<$2n(n^2-2n-1)+3n^2$<$-5(n^3-n^2-1)+n(n^2-n)$<$(n^2-1)(n+2)-n^2(n-3)$

which is the required pattern.