$$ a+b+bc+9a+10b+3c=\text{?} $$

$$ 10a+11b+(b+3)c $$

$$ 8y+45-34y-45z=\text{?} $$

$$ -26y+45-45z $$

Multiplication of 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: $7\times X+13\times Y=7X+13Y$

Detailed explanation

Start practice

Test yourself on variables and algebraic expressions!

$3x+4x+7+2=\text{?}$

Practice more now

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

Here are some examples

$8\times X=8X$
$X\times Y=XY$
$-3\times\left(5+6\right)=-3\left(5+6\right)$
$8\times\left(X-5\right)=8\left(X-5\right)$
$\left(5-a\right)\times\left(3+4\right)=(5-a)\left(3+4\right)$

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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Test your knowledge

Question 1

$3z+19z-4z=\text{?}$

Question 2

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

Question 3

Are the expressions the same or not?

$$ 3+3+3+3 $$

$3\times4$

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.

Examples and exercises with solutions for multiplying algebraic expressions

examples.example_title

$18x-7+4x-9-8x=\text{?}$

examples.explanation_title

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

$18x-8x+4x-7-9=$

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:

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

$14x-16$

examples.solution_title

$14x-16$

examples.example_title

$7.3\cdot4a+2.3+8a=\text{?}$

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:

$7.3×4a + 2.3 + 8a =$

$29.2a + 2.3 + 8a =$

$37.2a + 2.3$

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

$37.2a+2.3$

Do you know what the answer is?

Question 1

Are the expressions the same or not?

$$ 18x $$

$$ 2+9x $$

Question 2

$$ x+x= $$

Question 3

$$ 5+8-9+5x-4x= $$

Start practice