How to Simplify an Algebraic Expression?

Grade 7 Math Worksheets

Simplifying algebraic expressions involves combining like terms, removing parentheses, factoring out common factors, and performing various operations according to the rules of algebra.

Table of Contents:

Simplifying Expressions
Steps to simplify Algebraic Expressions
Solved Examples
FAQs

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How to Simplify an Algebraic Expression? - Grade 7 Math Worksheet PDF

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Simplifying Expressions

Simplifying algebraic expressions involves combining like terms, removing parentheses, factoring out common factors, and performing various operations according to the rules of algebra. The process helps to make the expressions easier to work with, evaluate, or solve equations involving those expressions.

By simplifying algebraic expressions, we can gain a clearer understanding of the underlying mathematical relationships and make calculations more efficient. It is an essential skill in various areas of mathematics, including algebra, calculus, and other branches of advanced mathematics.

Steps to Simplify Algebraic Expressions

Step 1: Solve parentheses by adding/subtracting like terms inside and by multiplying the terms inside the brackets with the factor written outside. Simplify parentheses by using the distributive property, i.e., multiplying the term outside the parentheses with each term inside. For example, 2x(x + y) simplifies to 2x^2 + 2xy.

Step 2: Use the exponent rules to simplify terms containing exponents.

Step 3: Add or subtract the like terms.

Step 4: At last, write the expression obtained in the standard form (from highest power to the lowest power).

Steps to Simplify Algebraic Expressions

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Solved Example

Expression: 2x + 3 – x

To simplify this expression, we’ll follow the steps mentioned earlier:

Step 1: Combine like terms.

In this expression, we have two terms with ‘x’ (2x and -x), and we have a constant term 3. We can combine the like terms by adding or subtracting their coefficients.

2x + 3 – x = (2x – x) + 3

Simplifying the terms, we get:

2x – x + 3

Step 2: Perform operations.

Now, we can simplify the expression further by performing the subtraction operation between 2x and x.

2x – x + 3 = x + 3

So, the simplified form of the expression 2x + 3 – x is x + 3.

We have combined the like terms (2x and -x) to get the simplified expression x + 3, where ‘x’ represents the variable and 3 is the constant term.

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FAQS

What is the purpose of simplifying algebraic expressions?

Simplifying algebraic expressions helps make them easier to work with, evaluate, or solve equations involving those expressions. It allows for a clearer understanding of the underlying mathematical relationships and can make calculations more efficient.

What are the basic steps to simplify an algebraic expression?

The basic steps to simplify an algebraic expression include combining like terms, removing parentheses using the distributive property, rearranging terms, factoring out common factors, and simplifying further if possible.

How do I combine like terms?

To combine like terms, add or subtract their coefficients while keeping the variable(s) and exponent(s) unchanged. For example, 3x + 2x can be combined to give 5x.

What is the distributive property, and how is it used in simplification?

The distributive property allows us to multiply a number or term to each term inside parentheses. For example, in the expression 2(3x + 4), we distribute the 2 to get 6x + 8.

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