Which expression is equivalent to 15b^2 - 8b^2?

1. INFER what operation is needed

• Given: \(15b^2 - 8b^2\)
• Both terms have the same variable part (\(b^2\)), so they are like terms
• The subtraction sign tells us to subtract the second coefficient from the first

2. INFER the combining rule application

• For like terms, we combine coefficients while keeping the variable part unchanged
• This becomes: \((15 - 8)b^2\)
• Calculate: \(15 - 8 = 7\)
• Result: \(7b^2\)

Answer: B (\(7b^2\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand which operation to apply when combining like terms.

Some students see the subtraction sign and think "I need to do something different" but then get confused about what operation to actually perform. They might add the coefficients instead (\(15 + 8 = 23\)) because they focus on "combining" rather than following the subtraction operation shown.

This may lead them to select Choice C (\(23b^2\))

Second Most Common Error:

Poor INFER execution: Students think they need to multiply when they see two algebraic terms next to each other.

Rather than recognizing this as subtraction of like terms, they interpret it as needing to multiply the coefficients: \(15 \times 8 = 120\). This stems from confusion about when to add/subtract coefficients versus when to multiply terms.

This may lead them to select Choice D (\(120b^2\))

The Bottom Line:

The key challenge is recognizing that like terms combine through coefficient operations while the variable part stays exactly the same. Students who haven't mastered this fundamental algebra rule often apply the wrong operation or overcomplicate a straightforward problem.