Subtraction of algebraic expressions is subtracting one expression from another expression. A detailed explanation is given about the Subtraction of algebraic expressions in this article. Go through each step of solving problems and understand how simply a Subtraction of algebraic expressions problem can be solved. Students can get complete knowledge of Algebraic Expressions by referring to this page.
How to Find Subtraction of Algebraic Expressions?
Follow the below-listed steps to Subtract Algebraic Expressions and arrive at the solution easily. They are along the lines
- Write the given expressions in standard form.
- After that arrange one expression under another expression with the like terms come in the same column.
- The main part of the subtraction of algebraic expressions is changing the sign of every individual term of the second expression to get the inverse of the expression.
- Lastly, add the like terms and get the final expression.
Subtraction of Algebraic Expressions Solved Examples
1. Subtract 3a + 4b – 2c from 5a – 2b + 2c
Solution:
Note down both given expressions and rearrange them if required.
3a + 4b – 2c = 3a + 4b – 2c
5a – 2b + 2c = 5a – 2b + 2c
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
5a – 2b + 2c
3a + 4b – 2c
Change the signs of each term available in the second row and fins the inverse of the second expression.
3a + 4b – 2c = -(3a + 4b – 2c) = – 3a – 4b + 2c
Add the like terms by arranging two expressions in columns to get the final expression.
5a – 2b + 2c
– 3a – 4b + 2c
—————————-
2a – 6b + 4c
The required expression is 2a – 6b + 4c
2. Subtract 4x² – 7x – 5 from 6 + 2x – 3x².
Solution:
Note down both given expressions and rearrange them if required.
6 + 2x – 3x² = – 3x² + 2x + 6
4x² – 7x – 5 = 4x² – 7x – 5
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
– 3x² + 2x + 6
4x² – 7x – 5
Change the signs of each term available in the second row and fins the inverse of the second expression.
4x² – 7x – 5 = -(4x² – 7x – 5) = – 4x² + 7x + 5
Add the like terms by arranging two expressions in columns to get the final expression.
– 3x² + 2x + 6
– 4x² + 7x + 5
—————————-
– 7x² + 9x + 11
The required expression is – 7x² + 9x + 11
3. Subtract 4x + 2y – 4z from 10x – 6y + 2z
Solution:
Note down both given expressions and rearrange them if required.
10x – 6y + 2z = 10x – 6y + 2z
4x + 2y – 4z = 4x + 2y – 4z
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
10x – 6y + 2z
4x + 2y – 4z
Change the signs of each term available in the second row and fins the inverse of the second expression.
4x + 2y – 4z = -(4x + 2y – 4z) = – 4x – 2y + 4z
Add the like terms by arranging two expressions in columns to get the final expression.
10x – 6y + 2z
– 4x – 2y + 4z
—————————-
6x – 8y + 6z
The required expression is 6x – 8y + 6z
4. Subtract – 5ab + 2a² from 3a² + 9ab.
Solution:
Note down both given expressions and rearrange them if required.
– 5ab + 2a² = 2a² – 5ab
3a² + 9ab = 3a² + 9ab
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
3a² + 9ab
2a² – 5ab
Change the signs of each term available in the second row and fins the inverse of the second expression.
2a² – 5ab = -(2a² – 5ab) = – 2a² + 5ab
Add the like terms by arranging two expressions in columns to get the final expression.
3a² + 9ab
– 2a² + 5ab
—————————-
a² + 14ab
The required expression is a² + 14ab
5. Subtract 2x² – 5xy + 9y² – 4 from 7xy – 2x² – 4y² + 7.
Solution:
Note down both given expressions and rearrange them if required.
7xy – 2x² – 4y² + 7 = – 2x² + 7xy – 4y² + 7
2x² – 5xy + 9y² – 4 = 2x² – 5xy + 9y² – 4
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
– 2x² + 7xy – 4y² + 7
2x² – 5xy + 9y² – 4
Change the signs of each term available in the second row and fins the inverse of the second expression.
2x² – 5xy + 9y² – 4 = -(2x² – 5xy + 9y² – 4) = – 2x² + 5xy – 9y² + 4
Add the like terms by arranging two expressions in columns to get the final expression.
– 2x² + 7xy – 4y² + 7
– 2x² + 5xy – 9y² + 4
—————————-
– 4x² + 12xy – 13y² + 11
The required expression is – 4x² + 12xy – 13y² + 11
6. What should be subtracted from 3a³ – 5a² + 7a – 8 to obtain 2a² – 4a + 3 ?
Solution:
Let ‘S’ denote the required expression.
Given that S subtracted from 3a³ – 5a² + 7a – 8 to get 2a² – 4a + 3.
(3a³ – 5a² + 7a – 8) – S = 2a² – 4a + 3
S = (3a³ – 5a² + 7a – 8) – (2a² – 4a + 3)
Note down both given expressions and rearrange them if required.
3a³ – 5a² + 7a – 8 = 3a³ – 5a² + 7a – 8
2a² – 4a + 3 = 2a² – 4a + 3
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
3a³ – 5a² + 7a – 8
0 + 2a² – 4a + 3
Change the signs of each term available in the second row and fins the inverse of the second expression.
0 + 2a² – 4a + 3 = -(0 + 2a² – 4a + 3) = – 0 – 2a² + 4a – 3
Add the like terms by arranging two expressions in columns to get the final expression.
3a³ – 5a² + 7a – 8
– 0 – 2a² + 4a – 3
—————————-
3a³ – 7a² + 11a – 11
The required expression is 3a³ – 7a² + 11a – 11
7. Subtract 5a³ – 6a² + 2a – 10 from the sum of 5a³ + 6a² + 9 and 8a² – 4?
Solution:
Given that Subtract 5a³ – 6a² + 2a – 10 from the sum of 5a³ + 6a² + 9 and 8a² – 4.
Therefore, firstly, find the sum of 5a³ + 6a² + 9 and 8a² – 4.
Note down the like terms and then find the sum of the numerical coefficients of all terms.
5a³ + 6a² + 9 + 8a² – 4
Arrange the like terms together.
5a³ + 6a² + 8a² + 9 – 4
Now, find the sum of the numerical coefficients of all terms.
5a³ + 14a² + 5
The required expression is 5a³ + 14a² + 5.
Now, subtract 5a³ – 6a² + 2a – 10 from 5a³ + 14a² + 5.
Note down both given expressions and rearrange them if required.
5a³ + 14a² + 5 = 5a³ + 14a² + 5
5a³ – 6a² + 2a – 10 = 5a³ – 6a² + 2a – 10
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
5a³ + 14a² + 0.a + 5
5a³ – 6a² + 2a – 10
Change the signs of each term available in the second row and fins the inverse of the second expression.
5a³ – 6a² + 2a – 10 = -(5a³ – 6a² + 2a – 10) = – 5a³ + 6a² – 2a + 10
Add the like terms by arranging two expressions in columns to get the final expression.
5a³ + 14a² + 0.a + 5
– 5a³ + 6a² – 2a + 10
—————————-
0 + 20a² – 2a + 15
The required expression is 20a² – 2a + 15
8. What should be subtracted from 10a³ – 15a² + 9a – 21 to obtain 6a² – 14a + 36 ?
Solution:
Let ‘S’ denote the required expression.
Given that S subtracted from 10a³ – 15a² + 9a – 21 to get 6a² – 14a + 36.
(10a³ – 15a² + 9a – 21) – S = 6a² – 14a + 36
S = (10a³ – 15a² + 9a – 21) – (6a² – 14a + 36)
Note down both given expressions and rearrange them if required.
10a³ – 15a² + 9a – 21 = 10a³ – 15a² + 9a – 21
6a² – 14a + 36 = 6a² – 14a + 36
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
10a³ – 15a² + 9a – 21
0 + 6a² – 14a + 36
Change the signs of each term available in the second row and fins the inverse of the second expression.
0 + 6a² – 14a + 36 = -(0 + 6a² – 14a + 36) = – 0 – 6a² + 14a – 36
Add the like terms by arranging two expressions in columns to get the final expression.
10a³ – 15a² + 9a – 21
– 0 – 6a² + 14a – 36
—————————-
10a³ – 21a² + 23a – 57
The required expression is 10a³ – 21a² + 23a – 57
9. Subtract 21a³ – 3a² + 4a – 6 from the sum of 6a³ + 7a² + 15 and 7a² – 16?
Solution:
Given that Subtract Subtract 21a³ – 3a² + 4a – 6 from the sum of 6a³ + 7a² + 15 and 7a² – 16.
Therefore, firstly, find the sum of 6a³ + 7a² + 15 and 7a² – 16.
Note down the like terms and then find the sum of the numerical coefficients of all terms.
6a³ + 7a² + 15 + 7a² – 16
Arrange the like terms together.
6a³ + 7a² + 7a² + 15 – 16
Now, find the sum of the numerical coefficients of all terms.
6a³ + 14a² – 1
The required expression is 6a³ + 14a² – 1.
Now, subtract 21a³ – 3a² + 4a – 6 from 6a³ + 14a² – 1.
Note down both given expressions and rearrange them if required.
6a³ + 14a² – 1 = 6a³ + 14a² – 1
21a³ – 3a² + 4a – 6 = 21a³ – 3a² + 4a – 6
Write both expressions one below another such that the expressions will subtract each other with the like terms come in the same column.
6a³ + 14a² + 0.a – 1
21a³ – 3a² + 4a – 6
Change the signs of each term available in the second row and fins the inverse of the second expression.
21a³ – 3a² + 4a – 6 = -(21a³ – 3a² + 4a – 6) = – 21a³ + 3a² – 4a + 6
Add the like terms by arranging two expressions in columns to get the final expression.
6a³ + 14a² + 0.a – 1
– 21a³ + 3a² – 4a + 6
—————————-
– 15a³ + 17a² – 4a + 5
The required expression is – 15a³ + 17a² – 4a + 5