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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