Add, Subtract Polynomials

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.

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.

Two engineers are working on a project to optimize a network's data flow. Engineer A improves the network's efficiency with a polynomial improvement of (3x³ + 3x² – 4x + 5), while Engineer B finds another optimization represented by (x³ – 2x² + x – 4). What is the combined improvement to the network's efficiency when both optimizations are applied?

(4x³-5x²+3x)+(-2x³-x²+6x)

Add or Subtract to Simplify:
 (4x - 2x³) + (5x³ - 4x + 5)

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

Add or Subtract to Simplify:
(4x²+ x) - (x²+ 2x)

(7x² - 3x) + (5x² + x + 3)

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

Simplify (5x⁴ - 4x³ - 2x² + x - 19) - (x⁴ + 5x³ + 8x² + x + 5)