Multiplication of Algebraic Expressions - Examples, Exercises and Solutions

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×X+13×Y=7X+13Y 7\times X+13\times Y=7X+13Y

7×X+13×Y=7X+13Y

Practice Multiplication of 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

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

Video Solution

Answer

7x+9 7x+9

Exercise #4

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

Video Solution

Answer

18z 18z

Exercise #5

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

Video Solution

Answer

19+3X

Exercise #1

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

Video Solution

Answer

8X 8X

Exercise #2

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

Video Solution

Answer

4+X

Exercise #3

x+x= x+x=

Video Solution

Answer

2x 2x

Exercise #4

Are the expressions the same or not?

18x 18x

2+9x 2+9x

Video Solution

Answer

No

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 #1

Are the expressions the same or not?

20x 20x

2×10x 2\times10x

Video Solution

Answer

Yes

Exercise #2

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

Video Solution

Answer

11a+17b 11a+17b

Exercise #3

13a+14b+17c4a2b4b=? 13a+14b+17c-4a-2b-4b=\text{?}

Video Solution

Answer

9a+8b+17c 9a+8b+17c

Exercise #4

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

Video Solution

Answer

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

Exercise #5

35m+9n48m+52n=? 35m+9n-48m+52n=?

Video Solution

Answer

61n13m 61n-13m

Topics learned in later sections

  1. Domain of a Function