Which expression is equivalent to 11x^3 - 5x^3?

1. INFER what type of problem this is

• Given expression: \(11\mathrm{x}^3 - 5\mathrm{x}^3\)
• Both terms have the same variable part: \(\mathrm{x}^3\)
• This means they are like terms that can be combined

2. SIMPLIFY by combining the coefficients

• Keep the variable part (\(\mathrm{x}^3\)) unchanged
• Subtract the coefficients: \(11 - 5 = 6\)
• Result: \(6\mathrm{x}^3\)

Answer: B. \(6\mathrm{x}^3\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students add the coefficients instead of subtracting them.

They see "\(11\mathrm{x}^3 - 5\mathrm{x}^3\)" but treat the subtraction sign as if it were addition, calculating \(11 + 5 = 16\). This may lead them to select Choice A (\(16\mathrm{x}^3\)).

Second Most Common Error:

Conceptual confusion about exponent rules: Students incorrectly think they should multiply the exponents when combining like terms.

They might correctly subtract coefficients (\(11 - 5 = 6\)) but then think the exponents should be multiplied (\(3 \times 3 = 6\)), giving them \(6\mathrm{x}^6\). This may lead them to select Choice C (\(6\mathrm{x}^6\)).

The Bottom Line:

This problem tests the fundamental skill of combining like terms, which requires recognizing when terms can be combined (same variable part) and correctly performing arithmetic with the coefficients while leaving the variable part unchanged.