# ADDING AND SUBTRACTING POLYNOMIALS PRACTICE

To know adding and subtracting polynomials, we have to know about two terms.

i) Like terms

ii) Unlike terms

What are like terms ?

Like terms are the terms which have the same variables with same exponent for each variable.

What are unlike terms ?

Unlike terms will not have same variables or they will not have same exponents.

Simplify the following.

Problem 1 :

(5x2 – 2x + 7) + (x3 – 5x2 – x + 3)

Solution :

Given, (5x2 – 2x + 7) + (x3 – 5x2 – x + 3)

= 5x2 – 2x + 7 + x3 – 5x2 – x + 3

By combining like terms,

= x3 - 2x – x + 7 + 3

= x3 – 3x + 10

Problem 2 :

(x3 – x2 + x + 1) + (x3 + x2 - x - 1)

Solution :

Given, (x3 – x2 + x + 1) + (x3 + x2 - x - 1)

= x3 – x2 + x + 1 + x3 + x2 – x – 1

By combining like terms,

= x3 + x3

= 2x3

Problem 3 :

(2x4 + x2 - 1) + (x4 – x3 + x + 1)

Solution :

Given, (2x4 + x2 - 1) + (x4 – x3 + x + 1)

= 2x4 + x2 - 1 + x4 – x3 + x + 1

By combining like terms,

= 2x4 + x4 – x3 + x2 + x

= 3x4 – x3 + x2 + x

Problem 4 :

(x4 - 2x3 + 3x2 – 4x + 5) + (5x3 – x2 + 7x - 3)

Solution :

Given, (x4 - 2x3 + 3x2 – 4x + 5) + (5x3 – x2 + 7x - 3)

= x4 - 2x3 + 3x2 – 4x + 5 + 5x3 – x2 + 7x - 3

By combining like terms,

= x4 – 2x3 + 5x3 + 3x2 – x2 – 4x + 7x + 5 – 3

= x4 + 3x3 + 2x2 + 3x + 2

Problem 5 :

(2x3 + 3x2 – 5x + 1) + (6 – 2x + 3x2 – x3)

Solution :

Given, (2x3 + 3x2 – 5x + 1) + (6 – 2x + 3x2 – x3)

= 2x3 + 3x2 – 5x + 1 + 6 – 2x + 3x2 – x3

By combining like terms,

= 2x3 – x3 + 3x2 + 3x2 – 5x – 2x + 1 + 6

= x3 + 6x2 – 7x + 7

Problem 6 :

(4x2 – x + 3) – (3x2 + x + 1)

Solution :

Given, (4x2 – x + 3) – (3x2 + x + 1)

= 4x2 – x + 3 – 3x2 - x - 1

By combining like terms,

= 4x2 – 3x2 – x – x + 3 – 1

= x2 – 2x + 2

Problem 7 :

(2x3 + x2 + 5x - 7) – (x3 – 2x2 + 5x + 4)

Solution :

Given, (2x3 + x2 + 5x - 7) – (x3 – 2x2 + 5x + 4)

= 2x3 + x2 + 5x - 7 – x3 + 2x2 - 5x – 4

By combining like terms,

= 2x3 - x3 + x2 + 2x2 – 7 – 4

= x3 + 3x2 – 11

Problem 8 :

(9x4 + x3 + 2x - 3) – (5x4 + 7x2 – 2x + 3)

Solution :

Given, (9x4 + x3 + 2x - 3) – (5x4 + 7x2 – 2x + 3)

= 9x4 + x3 + 2x - 3 – 5x4 - 7x2 + 2x - 3

By combining like terms,

= 9x4 – 5x4 + x3 – 7x2 + 2x + 2x – 3 – 3

= 4x4 + x3 – 7x2 + 4x – 6

Problem 9 :

(5x2 + 7x + 1) + (2x2 + x - 3) + (x2 – 10x + 7)

Solution :

Given, (5x2 + 7x + 1) + (2x2 + x - 3) + (x2 – 10x + 7)

= 5x2 + 7x + 1 + 2x2 + x - 3 + x2 – 10x + 7

By combining like terms,

= 5x2 + 2x2 + x2 + 7x + x – 10x + 1 + 7

= 8x2 - 2x + 8

Problem 10 :

(x3 – x + 3) + (x2 – 3x + 4) + (2x3 – x2 + 5)

Solution :

Given, (x3 – x + 3) + (x2 – 3x + 4) + (2x3 – x2 + 5)

= x3 – x + 3 + x2 – 3x + 4 + 2x3 – x2 + 5

By combining like terms,

= x3 + 2x3 – x – 3x + 3 + 4 + 5

= 3x3 – 4x + 11

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