Explain why 45 x is an algebraic expression

A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:. We could write this more compactly using exponential notation. Exponential notation is used in algebra to represent a quantity multiplied by itself several times. The exponent tells us how many factors of the base we have to multiply. In the video below we show more examples of how to write an expression of repeated multiplication in exponential form.

Solution 1. To simplify an exponential expression without using a calculator, we write it in expanded form and then multiply the factors.

Skip to main content. Adding and subtracting like terms. If you have 3 pencil case with the same number x of pencils in each, you have 3 x pencils altogether.

This can be done as the number of pencils in each case is the same. The terms 3 x and 2 x are said to be like terms. Consider another example. The terms 2 xy and xy are like terms. Two terms are called like terms if they involve exactly the same pronumerals and each pronumeral has the same index. The distributive law explains the addition and subtraction of like terms. For example:. The terms 2 x and 3y are not like terms because the pronumerals are different.

The terms 3 x and 3x 2 are not like terms because the indices are different. There are no like terms for 2 y , so by using the commutative law for addition the sum is. The any-order principle for addition is used for the adding like terms. Because of the commutative law and the associative law for multiplication any-order principle for multiplication the order of the factors in each term does not matter.

Brackets fulfill the same role in algebra as they do in arithmetic. Brackets are used in algebra in the following way. Let x be the number. For a party, the host prepared 6 tins of chocolate balls, each containing n chocolate balls.

Each crate of bananas contains n bananas. Three bananas are removed from each crate. Five extra seats are added to each row of seats in a theatre. There were s seats in each row and there are 20 rows of seats. How many seats are there now in total? The following example shows the importance of following the conventions of order of operations when working with powers and brackets.

Multiplying algebraic terms involves the any-order property of multiplication discussed for whole numbers. Arrays of dots have been used to represent products in the module, Multiplication of Whole Numbers.

Let n be the number of dots in each row. If an array is m dots by n dots then there are mn dots. The pattern goes on forever. How many dots are there in the n th diagram?

The area of a 3 cm by 4 cm rectangle is 12 cm 2. Find the total area of the two rectangles in terms of x and y. The area of the rectangle to the left is xy cm 2 and the area of the rectangle to the right is 2 xy cm 2. The n th positive even number is 2 n. Write the following using algebra to see what y ou get. Show that the sum of the first n odd numbers is n 2. Quotients of expressions involving pronumerals often occur. We call them algebraic fractions we will meet this again in the modules, Special Expansions and Algebraic Fractions.

Dividing by 5 gives. When an expression contains more terms, it may be helpful to rearrange the terms so that like terms are together. The Commutative Property of Addition says that we can change the order of addends without changing the sum. So we could rearrange the following expression before combining like terms.

Skills to Develop Evaluate algebraic expressions Identify terms, coefficients, and like terms Simplify expressions by combining like terms Translate word phrases to algebraic expressions. Be prepared! Before you get started, take this readiness quiz.

If you missed this problem, review Example 2. Evaluate Algebraic Expressions In the last section, we simplified expressions using the order of operations. Solution In this expression, the variable is an exponent. Solution This expression contains two variables, so we must make two substitutions. Solution We need to be careful when an expression has a variable with an exponent. Solution The expression has four terms.

Definition: Like terms Terms that are either constants or have the same variables with the same exponents are like terms. Simplify Expressions by Combining Like Terms We can simplify an expression by combining the like terms. We can see why this works by writing both terms as addition problems.