Which expression is equivalent to \(14(\mathrm{x} - 9)\)? 14x - 126 14x - 9 14x + 126 14x + 9...

1. SIMPLIFY using the distributive property

• Given expression: \(14(\mathrm{x} - 9)\)
• Apply distributive property: \(\mathrm{a}(\mathrm{b} - \mathrm{c}) = \mathrm{ab} - \mathrm{ac}\)
• Distribute 14 to both terms inside the parentheses:
  • \(14 \times \mathrm{x} = 14\mathrm{x}\)
  • \(14 \times (-9) = -126\)

2. SIMPLIFY the final expression

• Combine the results: \(14\mathrm{x} + (-126) = 14\mathrm{x} - 126\)

Answer: A (\(14\mathrm{x} - 126\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Incomplete SIMPLIFY execution: Students distribute 14 to the first term \((\mathrm{x})\) but forget to distribute it to the second term \((-9)\).

They think: "14 times x is 14x, and then I still have -9, so the answer is 14x - 9."

This leads them to select Choice B (\(14\mathrm{x} - 9\)).

Second Most Common Error:

Sign error during SIMPLIFY: Students correctly distribute 14 to both terms but make a sign error with the subtraction.

They calculate: "\(14 \times \mathrm{x} = 14\mathrm{x}\) and \(14 \times 9 = 126\), so I get \(14\mathrm{x} + 126\)."

This leads them to select Choice C (\(14\mathrm{x} + 126\)).

The Bottom Line:

The distributive property requires careful attention to signs and complete distribution to all terms. The key insight is that \(14(\mathrm{x} - 9)\) means "14 times everything inside the parentheses," so both x AND -9 must be multiplied by 14.