Which expression is equivalent to 50x^2 + 5x^2?

1. TRANSLATE the problem information

• Given expression: \(\mathrm{50x^2 + 5x^2}\)
• We need to find an equivalent expression from the answer choices

2. TRANSLATE what this means mathematically

• Both terms have the same variable part (\(\mathrm{x^2}\))
• This means we have like terms that can be combined
• The operation between them is addition (+)

3. SIMPLIFY by combining like terms

• When adding like terms, add the coefficients and keep the variable part the same
• Coefficients: \(\mathrm{50 + 5 = 55}\)
• Variable part stays: \(\mathrm{x^2}\)
• Result: \(\mathrm{55x^2}\)

Answer: D. \(\mathrm{55x^2}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misinterpret the addition sign as multiplication and calculate \(\mathrm{50 \times 5 = 250}\), then write \(\mathrm{250x^2}\).

This reasoning comes from rushing through the problem and not carefully reading the operation symbol, or from confusion about when to multiply versus add coefficients.

This may lead them to select Choice A (\(\mathrm{250x^2}\))

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify that they need to combine like terms but make an arithmetic error, calculating \(\mathrm{50 + 5 = 10}\) (perhaps confusing addition with division: \(\mathrm{50 \div 5}\)) or \(\mathrm{50 + 5 = 45}\) (perhaps confusing addition with subtraction: \(\mathrm{50 - 5}\)).

This may lead them to select Choice B (\(\mathrm{10x^2}\)) or Choice C (\(\mathrm{45x^2}\))

The Bottom Line:

This problem tests whether students can distinguish between combining like terms (adding coefficients) versus other operations, while also requiring careful attention to the actual operation symbol in the expression.