Add and Subtract Polynomials Steps

Lisa and John are comparing their savings over the year. Lisa's savings can be represented by the polynomial (3- 2x + 2x²), indicating her savings in thousands over x months, while John's savings are represented by (4x -5 +3x²), also in thousands over x months. Calculate the difference between Lisa's and John's savings. 

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Bob is planning to expand his orchard. He currently has
(3x² - 3x + 2) apple trees and plans to plant more. After planting (x² - 2x + 1) apple trees, how many apple trees will Bob have in total?

• A
  4x³-2x²+2

• B
  4x² - 5x + 3

• C
  -2x³+2x+2

• D
  4x³-2x²-2

Dr. Smith, a mathematician, is analyzing the growth patterns of two different species of plants over time. She models the growth of each species with polynomial equations and decides to compare their growth by subtracting the polynomial equation of species B from species A: (5x⁴ – 4x³ – 2x² + x – 19) – (x⁴ + 5x³ + 8x² + x + 5)

• 4x⁴ – 9x³ – 10x² – 24

• 4x⁴ – 9x³ – 10x² – 2x – 24

• 4x⁴ – 9x³ – 10x² + 2x – 24

• -4x⁴ – 9x³ – 10x² – 24

Alice and Bob are playing with numbers. Alice writes down the equation 
(3- 2x + 2x²) and Bob writes down (4x -5 +3x²). Find the difference between Alice's and Bob's equations.

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

John is managing his budget for the month. He records his income as (3- 2x + 2x²) dollars and his monthly bills as (4x -5 +3x²) dollars. Calculate the difference between his income and bills. 

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Lisa is calculating the total expenses for her bakery's renovation project. She initially estimated the expenses as (4n⁴ - 8n + 4) dollars. However, after a detailed review, she found an overestimation of (8n² + 4n⁴ + 1) dollars in her calculation. What is the corrected total expenses?

• -8n² - 8n + 3 

• -7n² - 8n + 3 

• -6n² - 8n + 3

• -7n² - 4n + 3

At Lucy's Cafe, Lucy is working on the financials for the month. She applies the formula:
(6c³ + 6 - c⁴) - (8c³ - 6c⁴ + 2) to calculate her monthly expenses and profits, where c represents the number of coffee batches brewed. Simplify the expression to find the formula for her monthly financial calculation.

• 4c⁴ - 2c³ + 7

• 5c⁴ - 2c³ + 4

• c⁴ - 2c³ + 7

• 5c⁴ - 2c³ + 7

Sarah is planning a small party and is calculating the total cost of decorations and snacks she bought. She spent on decorations
 (5x + 2) dollars and on snacks
 (4x + 5) dollars. Combine like terms to find the total cost.

• 9x -7

• -9x-11

• 9x+7

• x+7

Bob and Sarah are planning to prepare two types of cookies for a local charity event. The first cookie recipe requires ingredients costing (2x² + 5x - 7) dollars, and the second cookie recipe requires ingredients costing (3 - 4x² + 6x) dollars. How much will the ingredients for both cookie types cost in total?

• 2x² + 3x +1

• -2x² - 11x -4

• 2x² + 5x -7

• -2x² + 11x -4