Question

Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 12x2 − 2xy + 3. The friends have already collected the following number of cans:

Jessa: 3x2
Tyree: 5x2 − 8
Ben: 2xy + 4

Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)

Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)

Answer 1

Part A

Add up the expressions for the collected amount of cans:

• 3x² + 5x² - 8 + 2xy + 4 =
• 8x² + 2xy - 4

Part B

The number of cans the friends still need to collect is the difference of the targeted expression and the one we obtained in part A.

• 12x² − 2xy + 3 - (8x² + 2xy - 4) =
• 12x² − 2xy + 3 - 8x² - 2xy + 4 =
• 4x²  + 7