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

8y+4534y45z=? 8y+45-34y-45z=\text{?}

Video Solution

Step-by-Step Solution

To solve this question, we need to remember that we can perform addition and subtraction operations when we have the same variable,
but we are limited when we have several different variables.
 

We can see in this exercise that we have three variables:
45 45 which has no variable
8y 8y and 34y 34y which both have the variable y y
and 45z 45z with the variable z z

Therefore, we can only operate with the y variable, since it's the only one that exists in more than one term.

Let's rearrange the exercise:

4534y+8y45z 45-34y+8y-45z

Let's combine the relevant terms with y y

4526y45z 45-26y-45z

We can see that this is similar to one of the other answers, with a small rearrangement of the terms:

26y+4545z -26y+45-45z

And since we have no possibility to perform additional operations - this is the solution!

Answer

26y+4545z -26y+45-45z

Exercise #3

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 #4

8x24x+3x= \frac{8x^2}{4x}+3x=

Video Solution

Step-by-Step Solution

Let's break down the fraction's numerator into an expression:

8x2=4×2×x×x 8x^2=4\times2\times x\times x

And now the expression will be:

4×2×x×x4x+3x= \frac{4\times2\times x\times x}{4x}+3x=

Let's reduce and get:

2x+3x=5x 2x+3x=5x

Answer

5x 5x

Exercise #5

Simplifica la expresión:

2x3x23xx4+6xx27x35= 2x^3\cdot x^2-3x\cdot x^4+6x\cdot x^2-7x^3\cdot 5=

Video Solution

Step-by-Step Solution

We'll use the law of exponents for multiplication between terms with identical bases:

aman=am+n a^m\cdot a^n=a^{m+n}

We'll apply this law to the expression in the problem:

2x3x23xx4+6xx27x35=2x3+23x1+4+6x1+235x3 2x^3\cdot x^2-3x\cdot x^4+6x\cdot x^2-7x^3\cdot 5=2x^{3+2}-3x^{1+4}+6x^{1+2}-35x^3

When we apply the above law to the first three terms from the left, while remembering that any number can always be considered as that number raised to the power of 1:

a=a1 a=a^1

And in the last term we performed the numerical multiplication,

We'll continue and simplify the expression we got in the last step:

2x3+23x1+4+6x1+235x3=2x53x5+6x335x3=x529x3 2x^{3+2}-3x^{1+4}+6x^{1+2}-35x^3=2x^5-3x^5+6x^3-35x^3=-x^5-29x^3

Where in the first stage we simplified the expressions in the exponents of the terms in the expression and in the second stage we combined like terms,

Therefore the correct answer is answer A.

Answer

x529x3 -x^5-29x^3

Exercise #6

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 #7

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

Video Solution

Answer

7x+9 7x+9

Exercise #8

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

Video Solution

Answer

18z 18z

Exercise #9

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

Video Solution

Answer

19+3X

Exercise #10

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

Video Solution

Answer

8X 8X

Exercise #11

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

Video Solution

Answer

4+X

Exercise #12

x+x= x+x=

Video Solution

Answer

2x 2x

Exercise #13

Are the expressions the same or not?

18x 18x

2+9x 2+9x

Video Solution

Answer

No

Exercise #14

Are the expressions the same or not?

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

3×4 3\times4

Video Solution

Answer

Yes

Exercise #15

Are the expressions the same or not?

20x 20x

2×10x 2\times10x

Video Solution

Answer

Yes