# How to Simplify Equations

Simplifying equations is often the first step to solving algebra equations. Some methods that can be used to simplify an equation are Combine Like Terms, Multiplication & Division of Terms, Removal of Brackets (Distributive Property) and Cross Multiplication.

The following diagrams show how to combine like terms to simplify an expression. Scroll down the page for more examples and solutions. ### Combine Like Terms

Like terms are terms that have the same variable part, i.e. they only differ in their coefficients. Combining like terms is very often required in the process of simplifying equations.

For examples:
2x and –5x are like terms.

a and are like terms.

6x and 5y are unlike terms.

Like terms can be added or subtracted from one another.
For example:
a + a = 2 × a = 2a    (We usually write 2 × a as 2a)

2a + 4a = 6a

a + a + a = 3a

2a + 4      (Unlike terms cannot be simplified)

4a + 3b    (Unlike terms cannot be simplified)

6a – 3a = 3a

8b – 8b = 0

5a – 3      (Unlike terms cannot be simplified)

6a – 4b    (Unlike terms cannot be simplified)

Example 1:
Simplify: 8xy – 5yx = 1

Solution:
Step 1: 5yx is the same as 5xy using the commutative property

Step 2: Since the right side is already simple, we can work on the left side expression
8xy – 5yx = 8xy – 5xy = 3xy

Putting back the left side and right side of the equation:
3xy = 1

Example 2:
Simplify: 7a + 5b – 6b + 8a + 2b = 0

Solution:
Step 1: Group together the like terms:
7a + 5b – 6b + 8a + 2b = 0
(7a + 8a) + (5b – 6b + 2b) = 0

Step 2: Then simplify:
15a + b = 0

Answer: 15a + b = 0

### Multiplication And Division Of Terms

The coefficients and variables of terms can be multiplied or divided together in the process of simplifying equations.

For examples:
3 × 4b = 3 × 4 × b = 12b

5a × 3a = 5 × a × 3 × a = 5 × 3 × a × a = 15a2    (using exponents)

Be careful!
a × a = a2< br> a + a = 2a   Example 1:
Simplify: 4a × 5a ÷ 2a = 60

Solution:
Step 1: Perform the multiplication and division Step 2: Isolate a ### Removal Of Brackets - Distributive Property

Sometimes removing brackets (parenthesis) allows us to simplify the expression. Brackets can be removed by using the distributive property. This is often useful in simplifying equations.

For example:
3(a – 3) + 4 = 3 × a + 3 × (-3) + 4 = 3a – 9 + 4 = 3a – 5

5 – 6 (b + 1) = 5 + ( – 6 ) × b + (– 6) × 1 = 5 – 6b – 6 = – 6b – 1

Example 1:
Simplify: 5(a – 4) + 3 = 8

Solution:
Step 1: Remove the brackets
5a – 20 + 3 = 8

Step 2: Isolate variable a
5a = 8 – 3 + 20
5a = 25 ### Cross Multiplication

Cross multiplication allows you to remove denominators from fractions in an equation. Note that this technique applies only towards simplifying equations, not to simplifying expressions.

For example, if you have the equation: then you can multiply the numerator of one fraction with the denominator of the other fraction (across the = sign) as shown: to obtain the equation
(2 × 6) = a × 3

Example 1:
Simplify: Solution:
Step 1:Cross Multiply
4 × a = 8 × 5
4a = 40

Step 2: Isolate variable a #### How To Solve Fraction Equations By Isolating The Variable Using Inverse Operations?

Have a look at the following video for more examples on simplifying equations.

#### How To Simplify And Solve Equations?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 