What is the difference of the polynomials? (5x³ + 4x²) - (6x² - 2x - 9) - (x³ + 6x² + 9) - (x³ + 2x²) - (5x³ - 2x² - 2x - 9) - (5x³ - 2x² + 2x + 9)

Solution:

Given, the polynomials are (5x³ + 4x²), (6x²- 2x - 9), (x³ + 6x² + 9), (x³ + 2x²), (5x³ - 2x² - 2x - 9), (5x³ - 2x² + 2x + 9).

We have to find the difference between the polynomials.

Step 1:

(5x³ + 4x2) - (6x²- 2x - 9)

= 5x³ + 4x2 - 6x² + 2x + 9

= 5x³ - 2x² + 2x + 9

Step 2:

(5x³ - 2x² + 2x + 9) - (x³ + 6x² + 9)

= 5x³ - 2x² + 2x + 9 - x³ - 6x² - 9

= 5x³ - x³ - 2x² - 6x² + 2x + 9 - 9

= 4x³ - 8x² + 2x

Step 3:

(4x³ - 8x² + 2x) - (x³ + 2x²)

= 4x³ - 8x² + 2x - x³ - 2x²

= 4x³ - x³ - 8x² - 2x² + 2x

= 3x³ - 10x² + 2x

Step 4:

(3x³ - 10x² + 2x) - (5x³ - 2x² - 2x - 9)

= 3x³ - 10x² + 2x - 5x³ + 2x² + 2x + 9

= 3x³- 5x³ - 10x² + 2x² + 2x + 2x + 9

= -2x³ - 8x² + 4x + 9

Step 5:

(-2x³ - 8x² + 4x + 9) - (5x³ - 2x² + 2x + 9)

= -2x³ - 8x² + 4x + 9 - 5x³ + 2x² - 2x - 9

= -2x³ - 5x³ - 8x² + 2x² + 4x - 2x + 9 - 9

= -7x³ - 6x² + 2x

Therefore, the difference between the given polynomials is -7x³ - 6x² + 2x.