Which expression is equivalent to 15 + y^2 - 6?y^2 + 6y^2 + 21y^2 + 9y^2 - 9y^2 - 21

1. INFER the solution strategy

• The question asks for an equivalent expression, which means we need to simplify the given expression
• Strategy: Look for like terms that can be combined

2. SIMPLIFY by identifying like terms

• Given expression: \(15 + \mathrm{y}^2 - 6\)
• Like terms present:
  • Constants: 15 and -6 (these can be combined)
  • Variable term: \(\mathrm{y}^2\) (stands alone)

3. SIMPLIFY by combining like terms

• Combine the constants: \(15 - 6 = 9\)
• Keep the variable term unchanged: \(\mathrm{y}^2\)
• Result: \(\mathrm{y}^2 + 9\)

Answer: C (\(\mathrm{y}^2 + 9\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Making arithmetic errors when combining constants

Students might calculate 15 - 6 incorrectly, such as:

• Adding instead of subtracting: \(15 + 6 = 21\)
• Other arithmetic mistakes leading to wrong values

This may lead them to select Choice B (\(\mathrm{y}^2 + 21\)) or other incorrect options.

The Bottom Line:

This problem tests the fundamental skill of combining like terms. While conceptually straightforward, students often make simple arithmetic errors when working with the constants, especially when subtraction is involved. The key is careful attention to signs and accurate arithmetic.