Simplifying Algebraic Expressions – Examples & Exercises
You may want to study the “simplifying algebraic expressions examples” in the next section before attempting the quiz below.
Simplifying Expressions – Exercises
Instructions: Simplify the expressions that follow. Then check your answers in the next section.1) 10x + 5y – 6x + 12 + 3y – 6
2) 12a – 15 + 3c – 14 + 14b – 6a + 10 – 8c – 20b
3) 5x(3x2y + 2)
4) \(\text 3 \times \frac{\sqrt{2}}{3}\)
5) \(\frac{a^2 + ab}{a}\)
Simplifying Expressions – Answers
Answer to question 1
1) The correct answer is: 4x + 8y + 610x + 5y – 6x + 12 + 3y – 6 =
10x – 6x + 5y
10x – 6x + 5y + 12 + 3y – 6 =
4x + 5y + 12 + 3y – 6 =
4x + 5y + 3y + 12
4x + 5y + 3y + 12 – 6 =
4x + 8y + 12 – 6 =
4x + 8y + 6
Answer to question 2
2) The correct answer is: 6a – 6b – 5c – 1912a – 15 + 3c – 14 + 14b – 6a + 10 – 8c – 20b =
12a – 6a – 15 + 3c – 14 + 14b
12a – 6a – 15 + 3c – 14 + 14b + 10 – 8c – 20b =
6a – 15 + 3c – 14 + 14b + 10 – 8c – 20b =
6a + 14b – 15 + 3c – 14
6a + 14b – 15 + 3c – 14 + 10 – 8c – 20b =
6a + 14b – 20b – 15 + 3c – 14 + 10 – 8c
6a + 14b – 20b – 15 + 3c – 14 + 10 – 8c =
6a – 6b – 15 + 3c – 14 + 10 – 8c =
6a – 6b + 3c – 15
6a – 6b + 3c – 15 – 14 + 10 – 8c =
6a – 6b + 3c – 8c – 15 – 14 + 10
6a – 6b + 3c – 8c – 15 – 14 + 10 =
6a – 6b – 5c – 15 – 14 + 10 =
6a – 6b – 5c + (–15 – 14 + 10) =
6a – 6b – 5c – 19
Answer to question 3
3) The correct answer is: 15x3y + 10x5x(3x2y + 2) =
(5x × 3x2y) + (5x × 2) =
15x3y + (5x × 2) =
15x3y + 10x
Answer to question 4
4) The correct answer is: \(\sqrt{2}\)\(\text 3 \times \frac{\sqrt{2}}{3} =\)
\(\frac{3 \times \sqrt{2}}{3} =\)
\(\sqrt{2}\)
Answer to question 5
5) The correct answer is: a + b\(\frac{a^2 + ab}{a} =\)
\(\frac{a(a + b)}{a} =\)
\(\frac{a \times (a + b)}{a} =\)
\(\text a + b\)
Simplifying Algebraic Expressions – Examples and Explanations
In order to learn the process of simplifying algebraic expressions, you need examples showing you how to combine like terms.
When you combine like terms on “simplifying expressions” problems on your algebra test, you usually have to add or subtract.
Look at the example that follows.
Example: Simplify 5x + 3y – 2x + 10 + 2y – 4
Answer: 3x + 5y + 6
Step 1: Simplify for one of the algebraic terms
First of all, we will rearrange the expression to put the x terms together.
5x + 3y – 2x + 10 + 2y – 4 =
5x – 2x + 3y – 2x + 10 + 2y – 4 =
5x – 2x + 3y + 10 + 2y – 4
Then perform the subtraction on the x term:
5x – 2x 3y + 10 + 2y – 4 =
3x + 3y + 10 + 2y – 4
Step 2: Simplify for the other algebraic terms
Next, we need to rearrange the expression to put the y terms together.
3x + 3y + 10 + 2y – 4 =
3x + 3y + 2y + 10 + 2y – 4 =
3x + 3y + 2y + 10 – 4
Then perform the addition on the y term:
3x + 3y + 2y + 10 – 4 =
3x + 5y + 10 – 4
Step 3: Simplify for the constants
You will remember from our post on algebraic terms, that constants are the terms in an expression that do not have variables.
So, in our expression 3x + 5y + 10 – 4, the integers 10 and –4 are the constants.
Finally, we need to perform the subtraction on the constants.
3x + 5y + 10 – 4 =
3x + 5y + 6
Step 4: Check your result
Check to see if any further simplification is possible.
In our previous step, we had the result of 3x + 5y + 6.
We can see from the expression above that there is only one x term, only one y term, and only one constant.
So, we have simplified the expression as much as possible.
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Simplifying Expressions on Your Exam
You will have several problems on simplifying expressions on your algebra test.
What is "Simplifying Algebraic Expressions"?
The phrase "simplifying expressions" means that you need to put an algebraic expression in its simplest form.
So, in order to simplify, you need to perform any mathematical operations that you can in the expression.
You may need to add, subtract, multiply, divide, simplify fractions, or deal with exponents or square roots when you are simplifying expressions.
If you have not already done so, you may want to have a look at our post on Order of Operations (PEMDAS) before you continue reading this post.
If you feel that need further practice with simplifying expressions, please see the following posts before you try the exercises in the next section:
Simplification - Advanced Problems
Further Exam Practice
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