A student simplifies (6b + 4r) – (2b + r) and says that the result is 4b + 5r. Explain the error and describe the correct steps to simplify the expression.

Answer:

The student did not distribute the negative when subtracting. Distributing the negative, the expression is equal to 6b + 4r – 2b – r. Then use the commutative property to rewrite it as 6b – 2b + 4r – r. Then you can use the distributive property to write as (6 – 2)b + (4 – 1)r, which simplifies to 4b + 3r.