Whether you're a student or a professional, IDNLearn.com has answers for everyone. Find the information you need quickly and easily with our reliable and thorough Q&A platform.
Sagot :
Let's simplify each expression one by one and determine their coefficients for [tex]\( n^2 \)[/tex]. Finally, we will arrange the simplified expressions in increasing order based on the coefficients of [tex]\( n^2 \)[/tex].
1. Simplify:
[tex]\[ -5(n^3 - n^2 - 1) + n(n^2 - n) \][/tex]
[tex]\[ = -5n^3 + 5n^2 + 5 + n^3 - n^2 \][/tex]
[tex]\[ = -4n^3 + 4n^2 + 5 \][/tex]
The coefficient of [tex]\( n^2 \)[/tex] is 4.
2. Simplify:
[tex]\[ (n^2 - 1)(n + 2) - n^2(n - 3) \][/tex]
[tex]\[ = n^3 + 2n^2 - n - 2 - n^3 + 3n^2 \][/tex]
[tex]\[ = 5n^2 - n - 2 \][/tex]
The coefficient of [tex]\( n^2 \)[/tex] is 5.
3. Simplify:
[tex]\[ n^2(n - 4) + 5n^3 - 6 \][/tex]
[tex]\[ = n^3 - 4n^2 + 5n^3 - 6 \][/tex]
[tex]\[ = 6n^3 - 4n^2 - 6 \][/tex]
The coefficient of [tex]\( n^2 \)[/tex] is -4.
4. Simplify:
[tex]\[ 2n(n^2 - 2n - 1) + 3n^2 \][/tex]
[tex]\[ = 2n^3 - 4n^2 - 2n + 3n^2 \][/tex]
[tex]\[ = 2n^3 - n^2 - 2n \][/tex]
The coefficient of [tex]\( n^2 \)[/tex] is -1.
Now, let's arrange the simplified expressions in increasing order based on the coefficient of [tex]\( n^2 \)[/tex]:
1. [tex]\( 6n^3 - 4n^2 - 6 \)[/tex] [tex]\(\quad (\text{coefficient of } n^2 \text{ is } -4)\)[/tex]
2. [tex]\( 2n^3 - n^2 - 2n \)[/tex] [tex]\(\quad (\text{coefficient of } n^2 \text{ is } -1)\)[/tex]
3. [tex]\( -4n^3 + 4n^2 + 5 \)[/tex] [tex]\(\quad (\text{coefficient of } n^2 \text{ is } 4)\)[/tex]
4. [tex]\( 5n^2 - n - 2 \)[/tex] [tex]\(\quad (\text{coefficient of } n^2 \text{ is } 5)\)[/tex]
Thus, the expressions in increasing order based on the coefficient of [tex]\( n^2 \)[/tex] are:
[tex]\[ 6n^3 - 4n^2 - 6, \quad 2n^3 - n^2 - 2n, \quad -4n^3 + 4n^2 + 5, \quad 5n^2 - n - 2 \][/tex]
1. Simplify:
[tex]\[ -5(n^3 - n^2 - 1) + n(n^2 - n) \][/tex]
[tex]\[ = -5n^3 + 5n^2 + 5 + n^3 - n^2 \][/tex]
[tex]\[ = -4n^3 + 4n^2 + 5 \][/tex]
The coefficient of [tex]\( n^2 \)[/tex] is 4.
2. Simplify:
[tex]\[ (n^2 - 1)(n + 2) - n^2(n - 3) \][/tex]
[tex]\[ = n^3 + 2n^2 - n - 2 - n^3 + 3n^2 \][/tex]
[tex]\[ = 5n^2 - n - 2 \][/tex]
The coefficient of [tex]\( n^2 \)[/tex] is 5.
3. Simplify:
[tex]\[ n^2(n - 4) + 5n^3 - 6 \][/tex]
[tex]\[ = n^3 - 4n^2 + 5n^3 - 6 \][/tex]
[tex]\[ = 6n^3 - 4n^2 - 6 \][/tex]
The coefficient of [tex]\( n^2 \)[/tex] is -4.
4. Simplify:
[tex]\[ 2n(n^2 - 2n - 1) + 3n^2 \][/tex]
[tex]\[ = 2n^3 - 4n^2 - 2n + 3n^2 \][/tex]
[tex]\[ = 2n^3 - n^2 - 2n \][/tex]
The coefficient of [tex]\( n^2 \)[/tex] is -1.
Now, let's arrange the simplified expressions in increasing order based on the coefficient of [tex]\( n^2 \)[/tex]:
1. [tex]\( 6n^3 - 4n^2 - 6 \)[/tex] [tex]\(\quad (\text{coefficient of } n^2 \text{ is } -4)\)[/tex]
2. [tex]\( 2n^3 - n^2 - 2n \)[/tex] [tex]\(\quad (\text{coefficient of } n^2 \text{ is } -1)\)[/tex]
3. [tex]\( -4n^3 + 4n^2 + 5 \)[/tex] [tex]\(\quad (\text{coefficient of } n^2 \text{ is } 4)\)[/tex]
4. [tex]\( 5n^2 - n - 2 \)[/tex] [tex]\(\quad (\text{coefficient of } n^2 \text{ is } 5)\)[/tex]
Thus, the expressions in increasing order based on the coefficient of [tex]\( n^2 \)[/tex] are:
[tex]\[ 6n^3 - 4n^2 - 6, \quad 2n^3 - n^2 - 2n, \quad -4n^3 + 4n^2 + 5, \quad 5n^2 - n - 2 \][/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.