## Distributive Property And Combining Like Terms Homework Hotline

In this course, you will be introduced to basic algebraic operations and concepts, as well as the structure and use of algebra. Topics include linear inequalities and graphing, exponents, polynomials, and rational expressions. You will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes solving algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing linear equations. You will apply these skills to solve real-world problems (word problems). Each unit will have its own application problems, depending on the concepts you have been exposed to. This course is also intended to provide you with a strong foundation for intermediate algebra and beyond. It will begin with a review of some math concepts formed in pre-algebra, such as ordering operations and simplifying simple algebraic expressions, to get your feet wet. You will then build on these concepts by learning more about functions, graphing of functions, evaluation of functions, and factorization. You will spend time on the rules of exponents and their applications in distribution of multiplication over addition/subtraction.

### Overview

Students can use the commutative, associative, and distributive properties of addition and multiplication to simplify algebraic expressions. Problems are more easily solved if compatible terms can be combined first. Some problems can then be solved mentally.

### Compatible Terms

Real numbers, whether whole or mixed, are constants that can be added, subtracted, multiplied or divided. The only exception is dividing by zero, which is undefined. Compatible terms can also be simplified, as long as each term has the same variable or variables at the same degree. The terms 2x + 4x can be combined to equal 6x, and the terms 3y^{2}– 8y^{2 }equal -5y^{2}. However, 2x + 3z cannot be added, and 3x^{3 }+ 2x -4x is in its simplest form as 3x^{3} –2x.

### Commutative Property of Addition and Multiplication

According to the commutative property of addition or multiplication, the order of adding or multiplying numbers does not matter, as long as all of them are added or multiplied. For example, 30 + 40 = 70, and 40 +30 = 70. The law in math symbol language is a + b = b + a for addition, and ab=ba for multiplication. Similarly, 2x + 3y +3x – 2y is the same as 2x +3x +3y -2y. The commutative property is a useful tool in mental math. Suppose the column of figures is 51 + 25 + 25 +49 + 50. It can be rearranged as 51 +49 +25 + 25 +50 to equal 200.

### Associative Property of Addition and Multiplication

According to the associative property of addition or multiplication, the way numbers are grouped doesn’t matter, as long as all the numbers are added or multiplied. In math symbol language, (a + b) + c = a + (b +c). The associative property is also a tool that can be used in mental math. When the mental math problem 51 +49 +25 + 25 +50 was rearranged, it was also grouped, as (51 + 49) + (25 +25 + 50). Solving within parentheses, 100 +100 =200. Both the commutative and associative problems were used together to solve the problem. An expression such as 4x + 3y – .5y +7x can be rearranged as 4x +7x +3y -.5y and then regrouped as (4x +7x) + (3y – .5y) to equal 11x + 2.5y.

### Distributive Property

The long formal name of the Distributive Property is the Distributive Property of Multiplication over Addition, or the Distributive Property of Multiplication over Subtraction. In math symbol language, it means that (a +b)c = ac + bc, or (a-b)c = ac – bc. This property is very useful, because it allows monomials to be combined that use the same variables. For example, 3y + 2y = 5y because (3 +2)y equals 5y. Similarly, 17a -11a =6a because (17-11)a = 6a.

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