SIMPLIFYING POLYNOMIAL EXPRESSIONS

Simplify each expression.

Problem 1 :

3x² - 5x³ - x(2x² + 4x)

Solution :

= 3x² - 5x³ - x(2x² + 4x)

= 3x² - 5x³ - 2x³ - 4x²

By combining like terms,

= 3x² - 4x² - 5x³ - 2x³

= -x² - 7x³

= -7x³ - x²

Problem 2 :

a² - 2a + 5a³ + 1 – 10a

Solution :

= a² - 2a + 5a³ + 1 – 10a

= 5a³ + a² - 10a – 2a + 1

By combining like terms,

= 5a³ + a² - 12a + 1

Problem 3 :

17 – 3s² + 2s² - 5s³ + 5

Solution :

= 17 – 3s² + 2s² - 5s³ + 5

= -5s³ - 3s² + 2s² + 17 + 5

By combining like terms,

= -5s³ - s² + 22

Problem 4 :

17p + 8p³ - 4 – 5(p³ - 2)

Solution :

= 17p + 8p³ - 4 – 5(p³ - 2)

= 17p + 8p³ - 4 – 5p³ + 10

By combining like terms,

= 8p³ - 5p³ + 17p – 4 + 10

= 3p³ + 17p + 6

Problem 5 :

3(7r¹⁰ – 4r⁹ – 5r¹⁰)

Solution :

= 3(7r¹⁰ – 4r⁹ – 5r¹⁰)

= 21r¹⁰ – 12r⁹ – 15r¹⁰

By combining like terms,

= 6r¹⁰ – 12r⁹

Problem 6 :

11c⁵ – 9c⁶ + 15c⁵ – 13c⁶ + 5c⁶

Solution :

= 11c⁵ – 9c⁶ + 15c⁵ – 13c⁶ + 5c⁶

= 11c⁵ + 15c⁵ – 9c⁶ – 13c⁶ + 5c⁶

By combining like terms,

= 26c⁵ – 17c⁶

Problem 7 :

5m⁵ – 7m³ + 3m² - 5m⁵

Solution :

= 5m⁵ – 7m³ + 3m² - 5m⁵

By combining like terms,

= 5m⁵ – 5m⁵ - 7m³ + 3m²

= 3m² - 7m³

Problem 8:

5d² + 2d² - 8d³ - (2d² + 5d)

Solution :

= 5d² + 2d² - 8d³ - (2d² + 5d)

= 5d² + 2d² - 8d³ - 2d² - 5d

= -8d³ + 5d² + 2d² - 2d² - 5d

By combining like terms,

= -8d³ + 5d² - 5d

Problem 9 :

15x² - 7x⁴ + 25x³ - 10x⁴ + 35x³ - 5x⁴

Solution :

= 15x² - 7x⁴ + 25x³ - 10x⁴ + 35x³ - 5x⁴

= 15x² + 25x³ + 35x³ - 7x⁴ – 10x⁴ – 5x⁴

By combining like terms,

= 15x² + 60x³ - 22x⁴

Problem 10 :

2(n² + 2n² - 5n³) + 8n³ + 19

Solution :

= 2(n² + 2n² - 5n³) + 8n³ + 19

= 2n² + 4n² - 10n³ + 8n³ + 19

By combining like terms,

= 19 – 2n³ + 6n²

Problem 11 :

-5(b⁶ + 10) – 8(14 + b⁶)

Solution :

= -5(b⁶ + 10) – 8(14 + b⁶)

= -5b⁶ – 50 – 112 – 8b⁶

By combining like terms,

= -13b⁶ – 162

Problem 12 :

10 + 2y² - (8y³ - y² + 5y³)

Solution :

= 10 + 2y² - (8y³ - y² + 5y³)

= 10 + 2y² - 8y³ + y² - 5y³

By combining like terms,

= 10 + 2y² + y² - 8y³ - 5y³

= 10 + 3y² - 13y³

= -13y³ + 3y² + 10