If fractions are specified in an expression, we can use the distributive property and exponent rules to simplify such an expression. For example, 1/2 (x + 4) can be simplified to x/2 + 2. Let`s take another example to understand it. In this equation, you would start by simplifying the parenthetical part of the expression: 24-20. Simplifying an expression is just another way to solve a mathematical problem. When you simplify an expression, you`re essentially trying to write it in the simplest way. In the end, there should be no more addition, subtraction, multiplication or division to do. Take, for example, this expression: simplistic expressions mean paraphrasing the same algebraic expression without similar terms and in a compact way. To simplify the expressions, we combine all the similar terms and resolve all the given parentheses, if any, and then in the simplified expression, we are left with only other terms that cannot be reduced further. In this article, we`ll learn more about simplifying expressions. /en/algebra-topics/writing-algebraic-expressions/content/ In mathematics, simplifying expressions is a way to write an expression in its lowest form by combining all similar terms.
This requires familiarity with the concepts of arithmetic operations for algebraic expressions, fractions, and exponents. We follow the same PEMDAS rule to simplify algebraic expressions as we do for simple arithmetic expressions. In addition to PEMDAS, superscript rules and knowledge of operations for expressions should also be used, while simplifying algebraic expressions. This expression can be simplified by dividing each term by 2 as; 3 · x is 3x and 3 · 7 is 21. We can paraphrase the expression as follows: As with any problem, you must follow the order of operations when simplifying an algebraic expression. The order of operations is a rule that tells you the correct order to perform calculations. According to the order of operations, you need to solve the problem in this order: Solution: Using the rules to simplify expressions, 4ps – 2s – 3 (ps +1) – 2s can be simplified as: If acolor{#624F41} aa satisfies the above equation, what is the value of acolor{#624F41} aa? Let`s take an example for a better understanding. Simplify the expression: x (6 – x) – x (3 – x). There are two parentheses here, both of which have two different terms. So we will first solve the parentheses by multiplying x by the terms that are written there. X(6 – x) can be simplified to 6x – x2, and -x(3 – x) can be simplified to -3x + x2.
Now, if you combine all the terms, you get 6x – x2 – 3x + x2. In this expression, 6x and -3x are similar terms, and -x2 and x2 are similar terms. So if you add these two pairs of similar terms, you get (6x – 3x) + (-x2 + x2). If we simplify further, we get 3x, which will be the final answer. Therefore, x(6 – x) – x(3 – x) = 3x. Normally, in the order of operations, we would first simplify what is in parentheses. In this case, however, x+7 cannot be simplified because we cannot add a variable and a number. So what`s our first step? We need to learn how to simplify expressions, as they allow us to work more effectively with algebraic expressions and simplify our calculations.
To simplify algebraic expressions, follow these steps: Example 1: Find the simplified form of the expression formed by the following statement: “Addition of k and 8 multiplied by subtracting k of 16”. When faced with an expression like 4 x + 5 (3 x − 12), what do we do first? Let`s see: PEMDAS says work in parentheses first, but 3 x and 12 are different from the terms. Hmm, let`s try the distributive property: simplifying an expression means writing an equivalent expression that does not contain similar terms. This means that we will describe the expression with as few terms as possible. When simplifying expressions with fractions, we need to make sure that the fractions are in the simplest form and should only be included in the simplified expression. For example, (2/4)x + 3/6y is not the simplified expression, since fractions are not reduced to their lowest form. On the other hand, x/2 + 1/2y is in a simplified form, since fractions exist in the reduced form and both are different from terms. Note that the “intermediate terms” are eliminated, and we have the difference of two squares. Equations refer to statements that have an equal sign “=” between terms on the left and terms on the right. Solving equations means finding the value of the unknown variable. On the other hand, simplifying expressions means reducing the expression only to its lowest form.
It does not intend to determine the value of an unknown quantity. Using the distributive property, the specified expression can be written as 3/4x + y/2 (4x) + y/2 (7). To multiply fractions, we multiply numerators and denominators separately. Thus, y/2 × 4x/1 = (y × 4x)/2 = 4xy/2 = 2xy. And y/2 × 7/1 = 7y/2. Therefore, 3/4x + y/2 (4x + 7) = 3/4x + 2xy + 7y/2. All three are different terms, so it is the simplified form of the given expression. In other words, 15 is the easiest way to write 4 + 6 + 5. The two versions of the expression correspond to exactly the same quantity; One is just much shorter. Simplified expressions are much easier to process than those that have not been simplified. To simplify expressions with exponents, the rules of the exponents are applied to the terms. For example, (3×2)(2x) can be simplified to 6×3.
The exponent rule diagram that can be used to simplify algebraic expressions is given below: Sometimes when you simplify expressions, you may see something like this: Therefore, – k2 + 8k + 128 is the simplified form of the given expression. If that sounds like a big jump, don`t worry! All you need to simplify most expressions is basic arithmetic — addition, subtraction, multiplication and division — and the order of operations. Simplifying an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. 32 + 3 is 35 and 35 – 30 is 5. Our expression has been simplified – there is nothing more to do. The simplification of algebraic expressions refers to the process of reducing the expression to its lowest form. An example of simplifying algebraic expressions is given below: The distributive property states that an expression in the form x (y + z) can be simplified as xy + xz. It can be very useful while simplifying expressions. Take a look at the examples above and see if and how we used this property to simplify expressions. Let`s take another example of simplifying 4(2a + 3a + 4) + 6b with the distributive property.
Since both terms have the same exponents in the expression, we combine them; The process involves collecting similar terms, which involves adding or subtracting terms in an expression. To simplify this expression, let us first open the parenthesis by multiplying 4b by the two terms written there. This implies 2ab + 4b (b2) – 4b (2a). Using the exponent product rule, it can be written as 2ab + 4b3 – 8ab, which is equal to 4b3 – 6ab. In this way, we can simplify expressions with exponents using the rules of exponents. Learning how to simplify an expression is the most important step in understanding and mastering algebra. Simplifying expressions is a practical mathematical skill, as it allows us to transform complex or cumbersome expressions into simpler, more compact shapes. But before that, we need to know what an algebraic expression is. To simplify algebraic expressions, the following basic rules and steps are listed: Write the phrase by grouping similar terms. Solution: The instruction given gives the formed expression (k + 8)(16 – k).