To determine the correct description of the algebraic expression \(2 m^3 - 11\), let's analyze each option provided:
A. The difference of twice the cube of a number and 11
- This suggests we first find the cube of a number, multiply it by 2, and then subtract 11 from it. This matches the expression \(2 m^3 - 11\).
B. The difference of twice a number and 11 cubed
- This suggests we first find twice a number (which would be \(2m\)) and then subtract 11 cubed (\(11^3\)). This would result in \(2m - 1331\), which does not match the given expression.
C. Twice the cube of a number subtracted from 11
- This suggests we have 11 and then subtract twice the cube of a number from it. This would result in \(11 - 2m^3\), which does not match the given expression.
D. The cube of twice a number decreased by 11
- This suggests we first find twice a number (which gives \(2m\)), then cube it to get \((2m)^3 = 8m^3\), and finally subtract 11. This would be \(8m^3 - 11\) which does not match the given expression.
From this analysis, the correct answer is:
A. the difference of twice the cube of a number and 11
