How to Subtract Algebraic Expressions Using Like and Unlike Terms
Subtraction of algebraic expressions is identical to subtracting integers and calculating their difference, except that in the case of algebraic expressions, like and unlike terms are grouped together to solve the algebraic expressions questions, and then operations are conducted.
What are Algebraic Expressions?
An algebraic expression (or variable expression) is a phrase that has been combined using operations like addition, subtraction, multiplication, division, and so on. 5x+7 is an example of an algebraic expression. We may divide algebraic expression terms into two types: like and unlike terms.
Like terms are those that contain the same variable raised to the same power. Similarly, only the numerical factor can be changed.
Unlike terms are those that have distinct variables or the same variable raised to various powers.
What is The Subtraction of Algebraic Expressions?
To subtract two or more algebraic expressions, the terms in an algebraic expression must be classified into two types: similar and unlike terms. Then add up the like words and decrease them suitably. The horizontal approach demands writing the expressions to be subtracted below the expression from which they are to be subtracted. Similar words are listed below each other. Each term to be removed has its sign inverted, and the resultant expression is added normally.
How do Subtract Algebraic Expressions?
Subtraction of algebraic expressions can be done using the horizontal and the column method.
Horizontal Method: In this method the like expressions are grouped together and subtracted inside the brackets. The, unlike expressions, is written as it is.
Column Method: In this method both the expressions are written one below another one keeping the like expressions in the same column.
Sample Questions
1. If there is a negative sign outside the bracket and also inside the bracket. Then will the sign of the expression change?
a. Yes
b. No
Ans: Yes
Explanation: the sign inside the bracket will change when we will remove the bracket as two negatives make one positive sign. So the expression will change into a positive expression.
2. If there is a positive sign outside the bracket and a negative sign inside the bracket. Will there be a change in the sign of the expression?
a. Yes
b. No
Ans: Yes
Explanation: There would be a change in the sign of the expression as one positive and one negative results in negative. So the expression will change into negative expressions.
3. The expression consists of like numbers?
a. Yes
b. No
Ans: No
Explanation: The expression consists of the terms with different powers on them making them, unlike numbers. For them to be like they should have the same power.
Conclusion
It is usually best to remove two expressions at once. Never use the column technique to add three or more phrases together. If there is a negative sign outside the brackets, the operators inside the brackets must be reversed. We consider it positive if there is no sign written with the first term of the algebraic equation. 3x, for example, is equivalent to +3x.
FAQs on Subtraction of Algebraic Expressions with Rules and Examples
1. What is subtraction of algebraic expressions?
Subtraction of algebraic expressions is the process of finding the difference between two expressions by subtracting their like terms.
In algebra, you subtract expressions by:
- Removing brackets carefully.
- Changing the signs of the terms in the expression being subtracted.
- Combining like terms (same variables with same powers).
For example: (3x + 5) − (x + 2) = 3x + 5 − x − 2 = 2x + 3.
2. How do you subtract algebraic expressions step by step?
To subtract algebraic expressions, change the signs of the second expression and then combine like terms.
Steps:
- Write the expressions with brackets.
- Distribute the negative sign to all terms inside the second bracket.
- Combine like terms.
Example: (5x − 3) − (2x + 4)
= 5x − 3 − 2x − 4
= (5x − 2x) + (−3 − 4)
= 3x − 7.
3. What are like terms in algebra?
Like terms are terms that have the same variables raised to the same powers.
Examples of like terms:
- 4x and −2x
- 3a² and 7a²
Examples of unlike terms:
- 3x and 3x²
- 5a and 5b
Only like terms can be added or subtracted in algebraic expressions.
4. Why do we change signs when subtracting algebraic expressions?
We change signs because subtracting an expression means adding its additive inverse.
When you subtract (a + b), it becomes −a − b. This ensures correct distribution of the negative sign.
Example: 7x − (3x − 2)
= 7x − 3x + 2
= 4x + 2.
5. Can you give an example of subtracting polynomials?
Subtracting polynomials means subtracting each corresponding like term after distributing the negative sign.
Example:
(4x² + 3x − 5) − (2x² − x + 1)
- Distribute the minus: 4x² + 3x − 5 − 2x² + x − 1
- Combine like terms:
(4x² − 2x²) + (3x + x) + (−5 − 1)
= 2x² + 4x − 6.
6. What is the formula for subtraction of algebraic expressions?
The general rule for subtraction of algebraic expressions is A − B = A + (−B).
This means:
- Keep the first expression the same.
- Change the signs of every term in the second expression.
- Combine like terms.
This rule applies to binomials, trinomials, and all polynomials.
7. What are common mistakes when subtracting algebraic expressions?
The most common mistake is forgetting to change the sign of every term inside the bracket.
Other common errors include:
- Not distributing the negative sign properly.
- Combining unlike terms.
- Ignoring powers of variables.
Always check that all signs are correctly changed before combining like terms.
8. How do you subtract algebraic fractions?
To subtract algebraic fractions, first find a common denominator and then subtract the numerators.
Steps:
- Identify the least common denominator (LCD).
- Rewrite each fraction with the LCD.
- Subtract the numerators.
- Simplify the result.
Example: x/3 − x/6
LCD = 6
= 2x/6 − x/6 = x/6.
9. What is the difference between adding and subtracting algebraic expressions?
The key difference is that subtraction requires changing the signs of the second expression before combining like terms.
In addition:
- Remove brackets and combine like terms directly.
In subtraction:
- Distribute the negative sign.
- Then combine like terms.
Both operations rely on correctly identifying like terms.
10. How do you subtract expressions with multiple variables?
To subtract expressions with multiple variables, subtract only the terms that have identical variables and powers.
Example:
(3x + 2y − z) − (x − y + 4z)
- Distribute the negative: 3x + 2y − z − x + y − 4z
- Combine like terms:
(3x − x) + (2y + y) + (−z − 4z)
= 2x + 3y − 5z.
