Question 1 (Essay Worth 10 points) (06.02 MC) Three friends, Jessa, Tyree and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by following number of cans Jessa: 3x^2 Tyree: 5x^2-8 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)

Part A: To find the total amount of canned food collected so far by the three friends, we need to add up the expressions representing the number of cans collected by each friend.<br /><br />Jessa's expression: $3x^{2}$<br />Tyree's expression: $5x^{2}-8$<br />Ben's expression: $2xy+4$<br /><br />To add these expressions, we need to combine like terms. In this case, we can combine the terms with $x^{2}$ and the terms with $xy$.<br /><br />$3x^{2} + (5x^{2} - 8) + (2xy + 4)$<br /><br />Combining like terms, we get:<br /><br />$3x^{2} + 5x^{2} - 8 + 2xy + 4$<br /><br />Simplifying further, we have:<br /><br />$8x^{2} + 2xy - 4$<br /><br />Therefore, the expression representing the amount of canned food collected so far by the three friends is $8x^{2} + 2xy - 4$.<br /><br />Part B: To find the expression representing the number of cans the friends still need to collect to meet their goal, we need to subtract the total amount of canned food collected so far from their goal.<br /><br />The goal is represented by the sum of the expressions for each friend:<br /><br />$3x^{2} + (5x^{2} - 8) + (2xy + 4)$<br /><br />Subtracting the expression from Part A, we get:<br /><br />$(3x^{2} + 5x^{2} - 8 + 2xy + 4) - (8x^{2} + 2xy - 4)$<br /><br />Simplifying the expression, we have:<br /><br />$3x^{2} + 5x^{2} - 8 + 2xy + 4 - 8x^{2} - 2xy + 4$<br /><br />Combining like terms, we get:<br /><br />$0x^{2} + 0xy - 8$<br /><br />Therefore, the expression representing the number of cans the friends still need to collect to meet their goal is $-8$.