When a problem is presented to us in writing, we can convert it into mathematical language (also called algebraic language) by transforming it into an algebraic expression. But what are algebraic expressions?

Variable: This is a letter that represents a numerical value, for example X X or Y Y . This letter refers to an unknown numerical value that we must work out. For example: if X+5=8 X+5=8 , then we can conclude that the numerical value of X X is 3 3 .

An algebraic expression is a combination of numbers and letters (representing unknown numbers) that includes operations such as addition, subtraction, multiplication, division, etc.

Each element of an algebraic expression is called an algebraic term, be it a variable, a constant, or a combination of a coefficient and one or more variables. If the expression contains only one term, it is known as a monomial, while those that contain two or more terms are polynomials.

There is no limitation to the amount of constant numbers, unknown variables, or operations that can appear in an algebraic expression. In addition, there does not always have to be a variable in the algebraic expression, although it will always have a certain numerical value.

Practice Algebraic Expressions

Examples with solutions for Algebraic Expressions

Exercise #1

18x7+4x98x=? 18x-7+4x-9-8x=\text{?}

Video Solution

Step-by-Step Solution

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

18x8x+4x79= 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:

18x8x=10x 18x-8x=10x 10x+4x=14x 10x+4x=14x 79=16 -7-9=-16 Remember, these two numbers cannot be added or subtracted, so the result is:

14x16 14x-16

Answer

14x16 14x-16

Exercise #2

7.34a+2.3+8a=? 7.3\cdot4a+2.3+8a=\text{?}

Video Solution

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= 7.3×4a + 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.

Answer

37.2a+2.3 37.2a+2.3

Exercise #3

9m3m2×3m6= \frac{9m}{3m^2}\times\frac{3m}{6}=

Video Solution

Step-by-Step Solution

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

9m×3m3m2×6= \frac{9m\times3m}{3m^2\times6}=

We will simplify and get:

9m2m2×6= \frac{9m^2}{m^2\times6}=

We will simplify and get:

96= \frac{9}{6}=

We will factor the expression into a multiplication:

3×33×2= \frac{3\times3}{3\times2}=

We will simplify and get:

32=1.5 \frac{3}{2}=1.5

Answer

0.5m 0.5m

Exercise #4

Are the expressions the same or not?

20x 20x

2×10x 2\times10x

Video Solution

Answer

Yes

Exercise #5

Are the expressions the same or not?

3+3+3+3 3+3+3+3

3×4 3\times4

Video Solution

Answer

Yes

Exercise #6

Are the expressions the same or not?

18x 18x

2+9x 2+9x

Video Solution

Answer

No

Exercise #7

x+x= x+x=

Video Solution

Answer

2x 2x

Exercise #8

5+89+5x4x= 5+8-9+5x-4x=

Video Solution

Answer

4+X

Exercise #9

5+0+8x5= 5+0+8x-5=

Video Solution

Answer

8X 8X

Exercise #10

11+5x2x+8= 11+5x-2x+8=

Video Solution

Answer

19+3X

Exercise #11

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

Video Solution

Answer

7x+9 7x+9

Exercise #12

3z+19z4z=? 3z+19z-4z=\text{?}

Video Solution

Answer

18z 18z

Exercise #13

Are the expressions the same or not?

0.5x×1 0.5x\times1

0.5x+0 0.5x+0

Video Solution

Answer

Yes

Exercise #14

Are the expressions the same or not?

15x30 15x-30

45155x+15x 45-15-5x+15x

Video Solution

Answer

No

Exercise #15

7a+8b+4a+9b=? 7a+8b+4a+9b=\text{?}

Video Solution

Answer

11a+17b 11a+17b