# Multiplication of Algebraic Expressions

🏆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: $7\times X+13\times Y=7X+13Y$

## Test yourself on variables and algebraic expressions!

Are the expressions the same or not?

$$3+3+3+3$$

$$3\times4$$

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

### Here are some examples

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

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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.

## Examples and exercises with solutions for multiplying algebraic expressions

### Exercise #1

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

### Step-by-Step Solution

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:

$14x-16$

$14x-16$

### Exercise #2

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

### Step-by-Step Solution

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.

$37.2a+2.3$

### Exercise #3

$\frac{9m}{3m^2}\times\frac{3m}{6}=$

### Step-by-Step Solution

According to the laws of multiplication, we must first simplify everything into one exercise:

$\frac{9m\times3m}{3m^2\times6}=$

We will simplify and get:

$\frac{9m^2}{m^2\times6}=$

We will simplify and get:

$\frac{9}{6}=$

We will factor the expression into a multiplication:

$\frac{3\times3}{3\times2}=$

We will simplify and get:

$\frac{3}{2}=1.5$

$0.5m$

### Exercise #4

Are the expressions the same or not?

$3+3+3+3$

$3\times4$

Yes

### Exercise #5

Are the expressions the same or not?

$20x$

$2\times10x$