When we subtract the like terms, we are providing an expression in its simplified form, which is referred to as simplifying an expression. This is a subtopic of algebra, which is a branch of mathematics. In this article, we’ll look into the 6th Grade Math Concept Subtraction of Like Terms and how to simplify it, solved examples on subtracting like terms explained clearly.
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What is Subtraction of Like Terms?
While adding and subtracting algebraic expressions is comparable to adding and subtracting numbers, we must arrange like and unlike terms together when dealing with algebraic expressions. When subtracting like terms, when all of the terms are negative, remove their coefficients while keeping the variables and power of the like terms constant.
How do you Subtract Like Terms?
We cannot remove two or more unlike terms from an algebraic equation. It is necessary to keep in mind that we can only remove similar terms when subtracting algebraic formulas. Subtraction of algebraic equations can be done in two ways: horizontally or vertically.
Rules for Subtracting Like Terms
Algebraic expressions can be subtracted in two ways, similar to how they are added. Check out the step by step process on how to subtract like terms
- When subtracting two or more algebraic expressions, it is best to write the expressions to be subtracted underneath the expression to be subtracted from.
- Similar terms are listed below each other. Each term to be removed has its sign inverted, and the resultant expression is added normally.
Example:
We need to subtract (−14x²−17x−10) and (−16x²−18x−14)
⇒(−14x²−17x−10) and (−16x²−18x−14)
Now we need to multiply the second parentheses term by -1 to get,
⇒−14x²−17x−10+16x²+18x+14
x² is now a grouping.
We have x, and constant terms.
⇒−14x²+16x²−17x+18x−10+14
Now, we may add,
⇒2x²−x+4
This is the expected answer.
Two quadratic polynomials are subtracted in this problem. When you’re adding or subtracting algebraic equations, you need to be aware of the terms like and unlike. Only like terms can be subtracted or added. The terms which have the same variables and exponents are called like terms, whereas unlike terms have distinct variables.
Subtracting Like Terms Examples
1. Subtract xy from 8xy.
In this case, 8xy and xy are like terms.
The outcome of subtracting two like terms is also a similar term, the numerical coefficient of which is produced by subtracting the numerical coefficients of like terms.
The coefficient difference = 8 – 1, [xy signifies 1xy]
As a result, 8xy – xy = 7xy
2. Subtract 5x from -8x
5x and -8x are equivalent words in this context.
= -8x (5x)
= -8x – 5x, [open the parentheses]
= -13x
3. Deduct -4x from -7x.
-4x and -7x are equivalent words in this context.
– = -7x (-4x)
= -7x + 4x [since negative times negative equals positive, -(-4x) = +3x]
= -3x
4. 9x – 5x – 7y – 4y
In this case, 9x and 5x are Like Terms
In addition, 7y and 4y are Like Terms
9x – 5x = 4x
7y – 4y = 3y
5. (2x + 3y – z) – (4x + 3y + z)
4x and 2x are Like Terms equivalent concepts in this context.
3y and -3y are Subtraction of Like Terms
In addition, the terms z and -z are Like Terms
Subtracting two or more similar words yields another like term whose numerical coefficient is the sum of these like terms’ numerical coefficients.
Now, by rearranging the like terms, we obtain
= 2x – 4x + 3y – 3y – z – z
= -2x + 0 – 2z, [Since, + 3y – 3y = 0]
= -2x – 2z
FAQs on Subtracting Like Terms
1. What Does Algebraic Expression Subtraction Mean in Math?
Subtraction of algebraic expressions needs to classify the terms of an algebraic expression as similar or unlike. Then we group all like terms together such that the simplified statement only contains, unlike terms.
2. What Is the Algebraic Terms Subtraction and Addition Rule?
The fundamental rule for adding and subtracting algebraic terms is to only add and subtract like terms. In addition, in the scenario of subtraction, if there is a negative sign outside of the bracket, we alter the operators of the terms inside the bracket and continue solving.
3. How Do You Subtract Algebraic Expressions With Exponents?
To subtract algebraic expressions using exponents, there is a simple rule. For instance, 3x³+9x³=12x³. Both the variables and their exponents should be the same so that you only need to execute the necessary operations on the coefficients, as we may combine when they have exactly the very same variables with absolutely the same powers.
4. What is the Definition of an Algebraic Expression?
An algebraic expression (or variable expression) is made up of variables and constants that are joined by operations like addition, subtraction, multiplication, division, and so on.