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Subtraction of Algebraic Expressions

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Last updated date: 13th Jul 2024
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Introduction

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

1. If there is a negative sign outside the bracket and also inside the bracket. Then will the sign of the expression change?

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?

Yes, there would be a change in the sign of the expression as one positive and one negative results in a negative. So, the expression will change into a negative expression.

3. Can more than two algebraic expressions be solved together?

More than two algebraic expressions can be solved together but it will make calculations a little difficult. So, we need to solve the expressions using the grouping method where all the terms have the same variable and the rest of the terms are grouped together and are then solved.

4. How do you solve rational algebra subtraction questions?

When adding or subtracting two rational formulas that have the same denominator:

Step 1: Subtract or add the numerators.

Step 2: Write the acquired result over the common denominator.

If the denominators are not the same, edit them to make them the same. In other words, to find a common denominator.

5. How can we Add or Subtract Exponents from Algebraic Expressions?

To add or subtract algebraic formulas using exponents, use this easy method. Both exponents and the powers must be the same so that you just need to execute the appropriate operations on the coefficients. With this, you can easily subtract or add the exponents.