"Simplifying Expressions" is the basic topic required for the students who would like to study Algebra in math.

Expression is an algebraic or mathematical statement involves numbers,one or more variables and the operation symbols like +,-, x ,÷.

Simplifying expressions means combining all x terms as one x term and combining all constant terms as one constant term.

Distribution means sharing something among other recipients. In other words multiply the number or a variable which is outside the parenthesis with the inner terms.

**Procedure of multiplying two polynomials with exponents**

We will multiply two or more polynomials in the following order.

(1) Symbol

(2) Number

(3) Variable

Let us see how it works

Multiply ( 5 x² ) and (-2 x³)

= ( 5 x² ) **x** (-2 x³)

= 10 x⁵

if we have only one x term then we have to put that x term as it is.

Problem 1:

Simplify the expression 7 (x - 3) + 2 (2x - 5) - 3(x - 5)

**Solution:**

7 (x - 3) + 2 (2x - 5) - 3(x - 5)

let us see how to simplify the given expression step by step

Step 1 :

Distributing the number which is outside the parenthesis with inner terms

= 7x - 21 + 4x - 10 - 3x + 15

Step 2 :

Combine the like terms

= 7x + 4x - 3x - 21 - 10 + 15

= 11x - 3x - 31 + 15

= 8x - 16

Problem 2:

Simplify the expression 4x - (2 + 4x) - 2 (x - 1) - 8 (x -3)

**Solution:**

= 4x - (2 + 4x) - 2 (x - 1) - 8 (x -3)

= 4x - 2 - 4x - 2x + 2 - 8x + 24

= 4x - 4x - 2x - 8x - 2 + 2 + 24

= -10x + 24

Problem 3 :

Simplify the expression (2x - 7)/5 + (x + 9)/15 - (2x -2)/5

**Solution :**

= (2 x - 7)/5 + (x + 9 )/15 - (2 x - 2 )/5

Now we are going to combine the like terms

Problem 4 :

Simplify the expression (3x+41)/2 + (x-3 )/5 -(9-2x)/6

**Solution :**

Now we are going to distribute the numbers which is out side the parenthesis to the inner terms.Then combine the like terms

- Like terms and unlike terms
- Markup and markdown
- Percents grater than 1
- Solving one step equations
- Combining like terms
- variable and expressions
- Simplifying radical expressions
- Simplifying fractions

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