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Ways to simplify algebraic expressions

simplify algebraic expressions

Simplify simplify algebraic expression in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory.

It is one of the earliest branches in the history of mathematics. The study of mathematical symbols and rules sometimes includes manipulating these mathematical symbols, according to the definition of algebra. Algebra covers a wide range of topics, from solving simple equations to studying abstractions. Algebra equations are found in many chapters of mathematics that students will learn in school. In addition, algebra has several formulae and identities.

What is algebra?

Algebra is an alphanumeric expression that helps in finding out the unknown value. It aids in the solution of mathematical equations and the calculation of unknown numbers such as bank interest, proportions, and percentages. One can rewrite the equations by using the variables in algebra to represent the unknown entities related to them.

In daily life, one can employ algebraic formulas to determine the distance and capacity of containers and calculate sales prices as needed. Algebra is useful for expressing a mathematical equation and relationship with the use of letters (variables) or other symbols (numeric operators) to represent the entities. The equation’s unknown quantities can be solved using algebraic expressions.

What are the branches of algebra?

Algebra is a unique branch of mathematics that lets one find the unknown value in a mathematical expression. These unknown figures are referred to as variables.

Equations are a crucial subject in algebra. To conduct arithmetic operations follows a set of rules. The criteria are used to interpret data sets that contain two or more variables. It is used to analyze a variety of objects in our environment.

One can utilize algebra without even realizing it. Elementary, abstract, linear, advanced, and commutative algebra are some of the sub-branches of algebra.

What do you understand by simplifying algebraic expressions?

Simplifying mathematical expressions implies rewriting the same algebraic statement compactly with no like terms. To simplify expressions, one must combine all like terms and solve all specified brackets, if any, until they are left with unlike terms that cannot be further reduced in the simplified expression.

As a result of simplifying an algebraic expression, the resulting value is that mathematical expression’s final product. It means it cannot be simplified or solved anymore.

What are the different terms used in algebraic expressions?

As understood, an algebraic expression contains numbers, alphabets, and various numeric operators (such as +, ÷, -, ×). Nevertheless, there are particular terms used while expressing an algebraic representation. They are – 

  • Coefficient – a coefficient is a value that remains unchanged in an algebraic expression. This value comes in association with the variable of the equation.
  • Variable – variable refers to an unknown quantity for which simplification is needed. Variables can be a, x, p, y, and so on.
  • Monomial – a monomial is a mathematical expression that has only one term. For example, 5a, 7x, 3z, and so on. 
  • Binomial – in binomial expression, only two terms are present. For example, 3a + 2, 4y + y, 7x + x, and so on.
  • Trinomial – trinomials are expressions that contain three terms. For example, 3x² + 4x + 7

How do simplify algebraic expressions?

Any algebraic expression will contain the above-mentioned constituents in its equation. Moreover, these components help in finding out the unknown value of the variable quantity.

Expressions are mathematical statements that comprise at least two terms, each of which contains either numbers, variables, or both, and are connected by an addition/subtraction operator. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It is a general rule for simplifying algebraic expressions.

Simplifying algebraic expressions is an important skill to learn. It is because it allows a person to efficiently solve mathematical expressions, therefore, helping them in particular calculations. The steps to simplify an algebraic expression are: 

  • Solve the brackets by adding or subtracting like terms.
  • When a term is given outside the bracket, one can multiply it with the terms inside the bracket.
  • If exponents are in the equation, solve them using the exponent rule.
  • Perform mathematical operations between the like terms.
  • At last, rewrite the algebraic expression in descending order (i.e., highest to lowest).

What do you understand about the BODMAS rule?

The BODMAS rule is a popular way to simplify complex mathematical expressions. It is an acronym that stands for Bracket, Order, Division Multiplication, Addition, and Subtraction.

A synonym of BODMAS is the PEMDAS rule which is used in certain regions. This rule stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

Explain the BODMAS rules

BODMAS is an effective method of solving or simplifying algebraic expressions. It illustrates what operations should be performed in what order when solving an expression.

According to the BODMAS rule, if an expression involves brackets, One must first solve or simplify the bracket, then ‘order’ (powers and roots), then division, multiplication, addition, and subtraction from left to right. If a person solves the issue in the wrong order, they will certainly get the wrong answer.

If the expression contains more than one operator, one can use the BODMAS. In this scenario, we must first simplify the words within the brackets from the innermost to the outermost brackets and any roots or exponents. Then, from left to right, conduct multiplication or division operations. Finally, use addition or subtraction to arrive at the correct solution.

What are the tips and rules for simplifying algebraic expressions?

Apart from the complexity of algebraic expressions, they are pretty easy to solve. If a person follows the exact order of simplifying algebraic equations, they are less likely to fail.

Following are the tips to successfully simplify an equation using the BODMAS rule.

  •  Identify the brackets and solve them
  •  Now, solve the exponent values by using the exponent law or the values containing root terms
  •  Perform the operations of division or multiplication from left to right
  •  Add or subtract the given terms from left to right

An individual needs to know the rules of simplifying an algebraic expression before solving it. Some basic rules are combined to facilitate the given algebraic expression. Some of the rules are given below:

  • If two or more terms with variables are given, first simplify them by adding their coefficients.
  • Open the brackets in the expression by using the distributive law.
  • If there is a negative operator outside the brackets, one can consider changing the signs of all the numeric terms inside that bracket. It will help them simplify it.
  • In other cases, if the sign outside the brackets is positive, one can consider removing the brackets and writing the terms inside it as it is.

How do simplify algebraic expressions with exponents?

Most algebraic expressions have exponents in their equations. However, to simplify these values, one must consider using exponent law. This specific law can help facilitate all the exponential values given in the algebraic expression.

For example: 3x² × 2x = 6x³

Another example of 2ab + 4b (b² – 2a) is taken.

Solution:

Open the brackets to simplify the expression. Now, multiply 4b by both the terms written inside the bracket.

= 2ab + 4b (b²) – 4b (2a)

Now, by using the exponent law of the product rule, we get:

= 2ab + 4b³ – 8ab 

It can be further simplified as-

= 4b³ – 6ab 

It is a simple way of solving any given algebraic expression with exponents.

How do simplify algebraic expressions with the distributive property?

As the name suggests, distributive property deals with distributing the values to simplify them. This particular property helps simplify an extended algebraic expression so that it can be easily calculated. 

For example: a (x + y)

By using the distributive property, it is simplified as:

= ax + ay

Another complex example can be the simplification of 3(2a + 3a + 2) + 7b, using the distributive property.

= 3(2a + 3a + 2) + 7b

= 6a + 9a + 6 + 7b

= 15a + 6 + 7b

As this expression cannot be simplified further, we must arrange it in descending order.

= 15a + 7b + 6

What do you understand about the distributive property of solving algebraic expressions?

Because a variable is merely a letter that denotes a real number, the properties of real numbers are fundamental in the study of algebra. The distributive property, in particular, asserts that given any absolute values a, b, and c, one should simplify the components of the parenthesis first.

When the elements of brackets are difficult to be simplified, use the distributive property to multiply each term within the parenthesis by the factor outside the parentheses. One can multiply and delete the parenthesis by using the distributive property.

Conclusion

It is important to learn how to simplify an algebraic expression. It is because knowing how to simplify mathematical expressions can help in studying various theories and calculations. Apart from this, simplification of mathematical expressions also helps understand the different laws and rules of the algebra.

Frequently Asked Questions

1. How do you simplify an expression in Algebra?

Ans. In algebra, we can simplify an expression by doing any of the following:

Taking common factors out of the denominator of a fraction

Dropping like terms from an equation

Adding and subtracting fractions with the same denominator

2. How do you solve algebraic expressions?

Ans. To solve algebraic expressions, you have to combine the like terms in the expression.
For example, if you have the expression x^3 – 2x + 6, then you can combine the like terms to get 3x^2 – 2x + 6. Then, you can simplify our expression by factoring out a common factor from each term and multiplying out the resulting binomials: 3(x – 2)^2(6).

3. What are some examples of algebraic expressions?

Ans. There are a lot of examples of algebraic expressions in the world. For example, when you’re cooking, you might write down the recipe as an algebraic expression. Another example is when you’re figuring out how much money to tip the pizza delivery guy: if he made a mistake on your order, and it cost him $5 to get it right, you could write this as a negative 5/12.

4. How do you simplify expressions?

Ans. You can simplify an expression by:

-identifying the subject and predicate of each sentence, then combining them into one sentence.

-adding or subtracting a variable to or from an expression or equation.

-combining terms in an expression that have the same variable.

5. What are some examples of algebraic expressions?

Ans. Some examples of algebraic expressions are:

a+b,(2x+3y)^2 and sin(x)+cos(y)

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