To determine which statement correctly describes the expression [tex]\( 2m^3 - 11 \)[/tex], let's analyze each option carefully:
1. A. the cube of twice a number decreased by 11
- This statement suggests that we are cubing twice a number first, and then subtracting 11. If we let the number be [tex]\( m \)[/tex], then the expression would be:
[tex]\[
(2m)^3 - 11
\][/tex]
Simplifying this, we get:
[tex]\[
8m^3 - 11
\][/tex]
Clearly, this does not match the given expression [tex]\( 2m^3 - 11 \)[/tex].
2. B. the difference of twice the cube of a number and 11
- This statement suggests that we are first finding twice the cube of a number, and then subtracting 11. If we let the number be [tex]\( m \)[/tex], the expression becomes:
[tex]\[
2(m^3) - 11
\][/tex]
Simplifying this, we get:
[tex]\[
2m^3 - 11
\][/tex]
This matches the given expression exactly.
3. C. the difference of twice a number and 11 cubed
- This statement suggests that we are first finding twice a number, and then subtracting the cube of 11. If we let the number be [tex]\( m \)[/tex], the expression becomes:
[tex]\[
2m - 11^3
\][/tex]
Simplifying this, we get:
[tex]\[
2m - 1331
\][/tex]
Clearly, this does not match the given expression [tex]\( 2m^3 - 11 \)[/tex].
4. D. twice the cube of a number subtracted from 11
- This statement suggests that we subtract twice the cube of a number from 11. If we let the number be [tex]\( m \)[/tex], the expression becomes:
[tex]\[
11 - 2m^3
\][/tex]
Clearly, this is not the same as [tex]\( 2m^3 - 11 \)[/tex].
After thoroughly analyzing all the options, the correct answer is:
B. the difference of twice the cube of a number and 11
