Identify the mistake and solve

Question

A student submitted the following problem but the solution is incorrect. • Identify the mistake. What did the student do wrong? • Solve the problem correctly. Sec. 12.5 #86 Simplify: 12c2 d – 2cd + 8cd2 – (-c2 d + 4cd) – (5cd – 2cd2 ) Incorrect solution: 12c2 d – 2cd + 8cd2 – (-c2 d + 4cd) – (5cd – 2cd2 ) 12c2 d – 2cd + 8cd2 – c2 d + 4cd – 5cd – 2cd2 12c2 d + 6cd2 –c2 d – 3cd

Answer 1

To simplify the given expression, we first remove the parentheses and change the signs of the terms inside the parentheses where necessary. Then, we combine like terms:

12c²d - 2cd + 8cd² - (-c²d + 4cd) - (5cd - 2cd²)

This simplifies to:

12c²d + c²d - 2cd - 4cd + 8cd² + 2cd² - 5cd

Combining like terms, we get:

(12c²d + c²d) + (-2cd - 4cd - 5cd) + (8cd² + 2cd²)

This further simplifies to:

13c²d - 11cd + 10cd²

Answer 2

12c²d - 2cd + 8cd² - (-c²d + 4cd) - (5cd - 2cd²)

= 12c²d - 2cd + 8cd² + c²d - 4cd - 5cd + 2cd² = 13c²d + 10cd² - 11cd

Correct answer was obtained as follows: minus signs were distributed across parentheses and then like terms were combined.