Multiplication of Algebraic Expressions

๐Ÿ†Practice variables and algebraic expressions

Multiplying algebraic expressions is the same as multiplying conventional numbers, and therefore, the rules we apply to these will also be applied to algebraic expressions.
In algebraic expressions that contain variables or parentheses, it is not necessary to write the multiplication sign.

For example: 7ร—X+13ร—Y=7X+13Y 7\times X+13\times Y=7X+13Y

7ร—X+13ร—Y=7X+13Y

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Test yourself on variables and algebraic expressions!

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Are the expressions the same or not?

\( 3+3+3+3 \)

\( 3\times4 \)

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Remember that the rules of multiplication for algebraic expressions are the same as the multiplication rules for numbers.

Here are some examples

  • 8ร—X=8X 8\times X=8X
  • Xร—Y=XY X\times Y=XY
  • โˆ’3ร—(5+6)=โˆ’3(5+6) -3\times\left(5+6\right)=-3\left(5+6\right)
  • 8ร—(Xโˆ’5)=8(Xโˆ’5) 8\times\left(X-5\right)=8\left(X-5\right)
  • (5โˆ’a)ร—(3+4)=(5โˆ’a)(3+4) \left(5-a\right)\times\left(3+4\right)=(5-a)\left(3+4\right)

If you are interested in this article, you might also be interested in the following articles:

  • Unknowns and algebraic expressions
  • The numerical value in algebraic expressions
  • Equivalent expressions / Equivalent algebraic expressions
  • Simplification of like terms / Simplification of similar elements
  • Order of basic operations: addition, subtraction, multiplication, and division
  • Commutative property of multiplication
  • Associative property of multiplication
  • The distributive property in the case of multiplication
  • Multiplication and division of real numbers
  • Abbreviated multiplication formulas

On the Tutorela website, you will find a variety of articles about mathematics.


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How many exercises should I practice?

Since each student has a different learning pace, the answer to this question is individual for each one.
The important thing is that you are aware of your level, and know if you need to practice the formulas more.
Anyway, to memorize the basic formula, it is recommended to do 10 exercises of basic and medium level. ย 


Examples and exercises with solutions for multiplying algebraic expressions

examples.example_title

18xโˆ’7+4xโˆ’9โˆ’8x=? 18x-7+4x-9-8x=\text{?}

examples.explanation_title

To solve the exercise, we will reorder the numbers using the substitution property.

18xโˆ’8x+4xโˆ’7โˆ’9= 18x-8x+4x-7-9=

To continue, let's remember an important rule:

1. It is impossible to add or subtract numbers with variables.

That is, we cannot subtract 7 from 8X, for example...

We solve according to the order of arithmetic operations, from left to right:

18xโˆ’8x=10x 18x-8x=10x 10x+4x=14x 10x+4x=14x โˆ’7โˆ’9=โˆ’16 -7-9=-16 Remember, these two numbers cannot be added or subtracted, so the result is:

14xโˆ’16 14x-16

examples.solution_title

14xโˆ’16 14x-16

examples.example_title

7.3โ‹…4a+2.3+8a=? 7.3\cdot4a+2.3+8a=\text{?}

examples.explanation_title

It is important to remember that when we have numbers and variables, it is impossible to add or subtract them from each other.

We group the elements:

 

7.3ร—4a+2.3+8a= 7.3ร—4a + 2.3 + 8a =

29.2a + 2.3 + 8a = 

37.2a+2.3 37.2a + 2.3

 

And in this exercise, this is the solution!

You can continue looking for the value of a.

But in this case, there is no need.

examples.solution_title

37.2a+2.3 37.2a+2.3

Do you know what the answer is?
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