Table of Content

• Basic Concepts of Algebraic Expressions
• Addition and Subtraction of Algebraic Expressions
• Practice Questions on Addition and Subtraction of Algebraic Expressions
• Worksheet on Addition and Subtraction of Algebraic Expressions
• Frequently Asked Questions

Arithmetic Operation	Statement	Algebraic Expression
Addition	“x plus 10″ “sum of x and 10″ “x more than 10″ “x increased by 10″	x + 10
Subtraction	“x minus 10″ “10 subtracted from x” “difference of x and 10″ “10 less than x” “x decreased by 10″	x – 10
Division	“x divided by 10″ “quotient of x and 10″	x / 10
Multiplication	“10 times x” “product of 10 and x”	10x

The above highlighted are some keywords in the given example statements that will help in identifying the arithmetic operation for an algebraic expression.

For Addition of Algeabric Expression

For Subtraction of Algeabric Expression

Practice Questions on Subtraction of Algebraic Expressions

Problem 1: Simplify (2x²– 5y + 2) – (5x² + 2x – 5)

Solution:

According to the question, we need to simplify (5x² + 2x – 5) – (2x² – 5y + 2)

= 5x² + 2x – 5 – 2x² + 5y – 2

= 5x² – 2x² + 2x + 5y – 5 – 2

= (5 – 2)x² + 2x + 5y + (-5 -2)

= 3x² + 2x + 5y – 7

So, 3x² + 2x + 5y – 7 is the simplified algebraic expression.

Problem 2: Simplify 6(a + 3b) – 2(a – b)

Solution:

According to the question, we need to simplify 6(a + 3b) – 2(a – b)

= 6a + 6(3b) – 2(a) -2(-b)

= 6a + 18b – 2a + 2b

= 6a – 2a + 18b + 2b

= (6 – 2)a + (18 + 2)b

= 4a + 20b

So, 4a + 20b is the simplified algebraic expression.

Problem 3: Find the difference of 7a + 8b + 3ab + 30 and 12b – 5a – 18ab + 10

Solution:

According to the question, we need to find

= (7a + 8b + 3ab + 30) – (12b – 5a – 18ab + 10)

= 7a + 8b + 3ab + 30 – 12b + 5a + 18ab – 10

= 7a + 5a + 8b – 12b + 3ab + 18ab + 30 – 10

= (7 + 5)a + (8 – 12)b + (3 + 18)ab + (30 – 10)

= 13a – 4b + 21ab + 20

So, 13a – 4b + 21ab + 20 is the obtained algebraic expression.

Problem 4: Simplify (3x – 4)² – 6xy + 7x – 9y + 10

Solution:

(3x – 4)² – 6xy + 7x – 9y + 10

= (9x² – 2(3x)(4) + 16) – 6xy + 7x – 9y + 10

= (9x² – 24x + 16) – 6xy + 7x – 9y + 10

= 9x² – 24x + 7x – 9y – 6xy + 16 + 10

= 9x² – 17x – 9y – 6xy + 26

So, 9x² – 17x – 9y – 6xy + 26 is the simplified algebraic expression.

Problem 5: Simplify 3x³ – 5y³ + xy² – 3xy² – 8x³

Solution:

Simplifying, 3x³ – 5y³ + xy² – 3xy² – 8x³

= 3x³ – 8x³ – 5y³ + xy² – 3xy²

= (3 – 8)x³ – 5y³ + (1 – 3)xy²

= -5x³ – 5y³ – 2xy²

Therefore, -5x³ – 5y³ – 2xy² is the simplified algebraic expression.

Problem 6: Subtract 3xy + 4x – 3y³ from 10y³ – 5xy + 10

Solution:

According to the question, we need to find

= (10y³ – 5xy + 10) – (3xy + 4x – 3y³)

= 10y³ – 5xy + 10 – 3xy – 4x + 3y³

= 10y³ + 3y³ – 4x – 5xy + 10

= 13y³ -4x – 5xy + 10

So, 13y³ -4x – 5xy + 10 is the obtained algebraic expression.

Practice Questions on Addition of Algebraic Expressions

Problem 1: Add 10p + 9(10s + 4t) + 12q and 12s – 4t

Solution:

According to the question,

= (10p + 9(10s + 4t) + 12q) + (12s – 4t )

= (10p + 90s + 36t + 12q) + (12s – 4t)

= 10p + 12q + 90s + 12s + 36t – 4t

= 10p + 12q + (90 + 12)s + (36 – 4)t

= 10p + 12q + 102s + 32t

So, the obtained solution is 10p + 12q + 102s + 32t.

Problem 2: Find the sum of 2m + 3n – p and 6n – 4p

Solution:

According to the question, we need to find,

(2m + 3n – p) + (6n – 4p)

= 2m + 3n – p + 6n – 4p

= 2m + 3n + 6n -p – 4p

= 2m + (3 + 6)n – (1 + 4)p

= 2m + 9n – 5p

So, 2m + 9n – 5p is the obtained algebraic expression.

Problem 3: Find the sum of 2x² – 5y² + 9 and 10y² – 3xy + 10

Solution:

To find sum of the two given algebraic expression, let’s add them, we get

= (2x² – 5y² + 9) + (10y² – 3xy + 10)

= 2x² – 5y² + 10y² + 9 + 10

= 2x² + (-5 + 10)y² + (9 + 10)

= 2x² + 5y² + 19

So, the obtained sum of given algebraic expression is, 2x² + 5y² + 19.

Problem 4: Simplify (x + y)² + 3(4x + 5xy) + 9y²

Solution:

(x + y)² + 3(4x + 5xy) + 9y²

= (x² + 1xy + y²) + (12x + 15xy) + 9y²

= x² + y² + 9y² + 1xy + 15xy + 12x

= x² + (1 + 10)y² + (1 + 15)xy + 12x

= x² + 11y² + 16xy + 12x

So, x² + 11y² + 16xy + 12x is the simplified algebraic expression.

Addition and Subtraction of Algebraic Expressions

Question1: Simplify 12m + 9n + 3(4m + 3n)²

Question2: Simplify 32(2x + 3y + 1) + 5xy + 13y – 26

Question3: Simplify x³ – y² + 8y³ + 4xy² – 11y²

Question4: Find sum of 24a + 12b – 13ab and 3a + 3b + 3

Question5: Add 10(2x + 3xy) + 12 and 4x² + 5xy

Question6: Subtract x² + y² – (x – y)² from 5x² + 4xy + 2y²

Question7: Find the difference of 3y + 24xy + 15 and 5y + 13xy + 9x – 20

Question8: Find the sum of 2(x + 3y) + 10 and 4(3x + y)

Question9: Subtract 3x² + 4xy – 9 from 5y² + 11x² – 2xy – 11

Question10: Subtract 20x + y from 10x – 15y + 2xy

Read More:

• Algebra Formulas
• Division of Algebraic Expressions
• Multiplication of Algebraic Expression
• How are Algebraic Expressions Formed?

Addition and Subtraction of Algebraic Expressions Practice Questions- FAQs

What are Algebraic Expressions?

Algebraic expression are variable expressions that contains number, variables, coefficients, terms and arithmetic operations such as addition, subtraction, division, multiplication, etc. For example, 2x + 3y + 10 is an algebraic expression, where 2x, 3y and 10 are terms and 2, 3 are coefficient of variables x and y respectively.

Is it possible to Add or Subtract Terms with Different Variables in an Algebraic Expression?

No, we can only add or subtract like terms. For example, 3x and 4x can be combined, but, we can not combine 3x and 4y in an algebraic expression as they have different variables.

How to Add Two Algebraic Expression?

To add two algebraic expressions, combine the coefficients of like terms in the expression and simplify to get the final result. For example, (2x + 3y) + (x + 5y) can be written as 2x + x + 3y + 5y which is equal to 3x + 8y.

How to Subtract Two Algebraic Expression?

To subtract two algebraic expressions, distribute the negative sign over the second algebraic expression and then combine the coefficients of like terms, followed by simplification to get the final result. For example, (2x – 3y) – (5x – 2y) can be written as, 2x – 3y – 5x + 2y, equal to -3x – y.

Is 2 an Algebraic Expression?

Yes, 2 is an algebraic expression which contains only one term.