# ADDING AND SUBTRACTING POLYNOMIALS

Adding and subtracting polynomials is like combining like terms.

Problem 1 :

(3x² - 4x + 8) + (2x – 7x² - 5)

Solution :

= (3x² - 4x + 8) + (2x – 7x² - 5)

Using distributive property.

= 3x² - 4x + 8 + 2x – 7x² - 5

By combining the like terms, we get

= 3x² - 7x² - 4x + 2x + 8 – 5

= -4x² - 2x + 3

Problem 2 :

(3n² + 13n³ + 5n) – (7n + 4n³)

Solution :

= (3n² + 13n³ + 5n) – (7n + 4n³)

= 3n² + 13n³ + 5n – 7n – 4n³

= 3n² + 13n³ - 4n³ + 5n – 7n

= 3n² + 9n³ - 2n

Problem 3 :

(2b² + 8ab³ + 4b) – (9b – 5ab³)

Solution :

= (2b² + 8ab³ + 4b) – (9b – 5ab³)

= 2b² + 8ab³ + 4b – 9b + 5ab³

= 2b² + 8ab³ + 5ab³ + 4b – 9b

= 2b² + 13ab³ - 5b

Problem 4 :

(6y² + 8y4 – 5y) – (9y4 - 7y + 2y²)

Solution :

= (6y² + 8y4 – 5y) – (9y4 - 7y + 2y²)

= 6y² + 8y4 – 5y – 9y4 + 7y – 2y²

= 8y4 – 9y4 + 6y² - 2y² - 5y + 7y

= -y4 + 4y² + 2y

Problem 5 :

(7y² + 2y - 3) + (2 – 4y + 5y²)

Solution :

= (7y² + 2y - 3) + (2 – 4y + 5y²)

= 7y² + 2y – 3 + 2 – 4y + 5y²

= 7y² + 5y² + 2y – 4y – 3 + 2

= 12y² - 2y – 1

Problem 6 :

(3x² + 5x + 2) – (4 – 2x) + (5x² + 7)

Solution :

= (3x² + 5x + 2) – (4 – 2x) + (5x² + 7)

= 3x² + 5x + 2 – 4 + 2x + 5x² + 7

= 3x² + 5x² + 5x + 2x + 2 - 4 + 7

= 8x² + 7x + 5

Problem 7 :

(-2x + 3) + (4x - 3)

Solution :

= (-2x + 3) + (4x - 3)

= -2x + 3 + 4x - 3

= -2x + 4x + 3 - 3

= 2x

Problem 8 :

(2x² + 2x - 4) + (x² + 3x + 7)

Solution :

= (2x² + 2x - 4) + (x² + 3x + 7)

= 2x² + 2x - 4 + x² + 3x + 7

= 2x² + x² + 2x + 3x – 4 + 7

= 3x² + 5x + 3

Problem 9 :

(3a² + a - 4) + (a² - 2a - 1)

Solution :

= (3a² + a - 4) + (a² - 2a - 1)

= 3a² + a – 4 + a² - 2a – 1

= 3a² + a² + a – 2a – 4 – 1

= 4a² - a – 5

Problem 10 :

(t² - 1) + (2t + 3)

Solution:

= (t² - 1) + (2t + 3)

= t² - 1 + 2t + 3

= t² + 2t - 1 + 3

= t² + 2t + 2

Problem 11:

(2x² + 3) + (x² - 2x - 1)

Solution:

= (2x² + 3) + (x² - 2x - 1)

= 2x² + 3 + x² - 2x – 1

= 2x² + x² - 2x + 3 – 1

= 3x² - 2x + 2

Problem 12:

(2x² + 5xy + 3y²) + (8x² - 7y²)

Solution:

= (2x² + 5xy + 3y²) + (8x² - 7y²)

= 2x² + 5xy + 3y² + 8x² - 7y²

= 2x² + 8x² + 5xy + 3y² - 7y²

= 10x² + 5xy – 4y²

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