Adding like terms in algebra
Introduction :
In algebra, Algebraic expressions are made by forming variables and constants. We simply use the arithmetic operations of addition, subtraction, multiplication and division on the variables and constants to form expressions.
For example, The expression 30ab + 6 is formed from the variables a and b and constants 30 and 6.
We can simplify the given expression by adding like terms or subtracting like terms.
Adding two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all the like terms.
Unlike terms cannot be added or subtracted the way like terms are added or subtracted.
Let us learn problems on Simplifying expressions.
Sample Problems on adding like terms in algebra:
Problem 1:
Add the two algebra expressions: 20x + 21 and 9x + 8
Solution:
Sum of the two algebra expressions: 20x + 21 + 9x + 8
Rearrange the expression by grouping like terms.
20x + 9x + 21 + 8
Adding like terms in the expression.
29x + 29
Hence, 20x + 9x + 21 + 8 = 29x + 29
Problem 2:
Add the two algebra expressions: 5x + 14 + 8z and 6x – 5
Solution:
Sum of the two expressions: 5x + 14 + 8z + 6x – 5
Rearrange the expression by grouping like terms.
5x + 6x + 8z + 14 – 5
Adding like terms in the expression.
11x + 8z + 9
Hence, 5x + 14 + 8z + 6x - 5 = 11x + 8z + 9
Problem 3:
Simplify Algebraic Expressions by combining like terms: 4a – 3b – 2ab – (a – b + ab) + 5ab + 2b – 2a
Solution:
The given expression: 4a – 3b – 2ab – (a – b + ab) + 5ab + 2b – 2a
Expand the expression.
4a – 3b – 2ab – a + b – ab + 5ab + 2b – 2a
Rearrange the expression by grouping like terms.
4a – a – 2a – 3b + b + 2b – 2ab – ab + 5ab
4a – 3a – 3b + 3b + 5ab – 3ab
Adding like terms in the expression.
a + 2ab
Hence, 4a – 3b – 2ab – (a – b + ab) + 5ab + 2b – 2a = a + 2ab .
Problem 4:
Simplify algebra expression by combining like terms: (5y2 + 6y – 7) – (9y – 2y2 – 3)
Solution:
The given expression: (5y2 + 6y – 7) – (9y – 2y2 – 3)
Expand the expression.
5y2 + 6y – 7 – 9y + 2y2 + 3
Rearrange the expression by grouping like terms.
5y2 + 2y2 + 6y – 9y – 7 + 3
Adding like terms in the expression.
7y2 – 3y - 4
Hence, (5y2 + 6y – 7) – (9y – 2y2 – 3) = 7y2 – 3y - 4.
Practice Problems On adding like terms in algebra:
Practice Problem 1:
Add the given algebra expressions: 2a + b – 5 , 2b – a + 5 and a – b + 5
Answer:
2a + 2b + 5.
Practice Problem 2:
Add the given expressions: 10m – 8n, 4n – 3m + 6 and 3m – 4mn – 7 .
Answer:
10m – 4n – 4mn – 1.
Practice Problem 3:
Simplify the algebra expression: 2p – (p – q) – 2q – (q – p)
Answer:
2p – 2q.
In algebra, Algebraic expressions are made by forming variables and constants. We simply use the arithmetic operations of addition, subtraction, multiplication and division on the variables and constants to form expressions.
For example, The expression 30ab + 6 is formed from the variables a and b and constants 30 and 6.
We can simplify the given expression by adding like terms or subtracting like terms.
Adding two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all the like terms.
Unlike terms cannot be added or subtracted the way like terms are added or subtracted.
Let us learn problems on Simplifying expressions.
Sample Problems on adding like terms in algebra:
Problem 1:
Add the two algebra expressions: 20x + 21 and 9x + 8
Solution:
Sum of the two algebra expressions: 20x + 21 + 9x + 8
Rearrange the expression by grouping like terms.
20x + 9x + 21 + 8
Adding like terms in the expression.
29x + 29
Hence, 20x + 9x + 21 + 8 = 29x + 29
Problem 2:
Add the two algebra expressions: 5x + 14 + 8z and 6x – 5
Solution:
Sum of the two expressions: 5x + 14 + 8z + 6x – 5
Rearrange the expression by grouping like terms.
5x + 6x + 8z + 14 – 5
Adding like terms in the expression.
11x + 8z + 9
Hence, 5x + 14 + 8z + 6x - 5 = 11x + 8z + 9
Problem 3:
Simplify Algebraic Expressions by combining like terms: 4a – 3b – 2ab – (a – b + ab) + 5ab + 2b – 2a
Solution:
The given expression: 4a – 3b – 2ab – (a – b + ab) + 5ab + 2b – 2a
Expand the expression.
4a – 3b – 2ab – a + b – ab + 5ab + 2b – 2a
Rearrange the expression by grouping like terms.
4a – a – 2a – 3b + b + 2b – 2ab – ab + 5ab
4a – 3a – 3b + 3b + 5ab – 3ab
Adding like terms in the expression.
a + 2ab
Hence, 4a – 3b – 2ab – (a – b + ab) + 5ab + 2b – 2a = a + 2ab .
Problem 4:
Simplify algebra expression by combining like terms: (5y2 + 6y – 7) – (9y – 2y2 – 3)
Solution:
The given expression: (5y2 + 6y – 7) – (9y – 2y2 – 3)
Expand the expression.
5y2 + 6y – 7 – 9y + 2y2 + 3
Rearrange the expression by grouping like terms.
5y2 + 2y2 + 6y – 9y – 7 + 3
Adding like terms in the expression.
7y2 – 3y - 4
Hence, (5y2 + 6y – 7) – (9y – 2y2 – 3) = 7y2 – 3y - 4.
Practice Problems On adding like terms in algebra:
Practice Problem 1:
Add the given algebra expressions: 2a + b – 5 , 2b – a + 5 and a – b + 5
Answer:
2a + 2b + 5.
Practice Problem 2:
Add the given expressions: 10m – 8n, 4n – 3m + 6 and 3m – 4mn – 7 .
Answer:
10m – 4n – 4mn – 1.
Practice Problem 3:
Simplify the algebra expression: 2p – (p – q) – 2q – (q – p)
Answer:
2p – 2q.
