## Evaluating Algebraic Expressions
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Hi everyone. This math educational post is on evaluating algebraic expressions. This particular topic may not be fun and does not have real world applications. The thing is though is that this is an important algebra topic for early high school math students.

Math text rendered in LaTeX with QuickLaTeX.com

<center><img src="https://cdn.pixabay.com/photo/2015/10/12/14/50/calculator-983900_960_720.jpg" /></center>
<center><a href="https://cdn.pixabay.com/photo/2015/10/12/14/50/calculator-983900_960_720.jpg">Pixabay Image Source</a></center>


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## Topics
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* Algebra Expressions
* Substitution of Values
* Following Order of Operations
* Harder Cases

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## Algebra Expressions
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An algebra expression is a quantity which contains a combination of numbers and unknown quantities. Examples include 2x, x + 7, 10x - 4, and x + pi. Note that an algebra expression does not contain an equal sign. There is no need to isolate for a variable.


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## Substitution Of Values
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When it comes to evaluating algebraic expressions, the concept of substituting unknown quantities (variables) with known values comes into play. 

In the algebraic expression x + 5, substituting x = 5 into x gives 5 +5 which is equal to 10. Substituting a different value such as 2 gives 2 + 5 = 7 which is a different value. 

When it comes to with more than one variable, you would need to be given values for those unknown variables. For example, substituting x = 2 and y = 1 in the algebraic expression of xy - 2y + 3x gives the following:

<center>https://quicklatex.com/cache3/d4/ql_f75606639169fbb527a9f97629b959d4_l3.png</center>


<center><img src="https://cdn.pixabay.com/photo/2016/02/19/11/36/classroom-1209820_960_720.jpg" /></center>
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## Following Order Of Operations
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With evaluating algebraic expressions, do remember that the algebra steps follows the order of operations. BEDMAS is for Brackets, Exponents followed by Division, Multiplication, Addition and Subtraction. Whenever there is a tie in multiplication and division, perform the operation that is first from left to right. Do the same with ties between addition and subtraction.

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**Example One**

Substituiting x = 2 in the algebraic expression 5x - 1 gives:

<center>https://quicklatex.com/cache3/42/ql_4b004892228190140773a7f2c631a242_l3.png</center>


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**Example Two**

Given the algebraic expression of 2(3x - 1) - 4, what would the expression be if x = -1?

<center>https://quicklatex.com/cache3/9e/ql_5c10317459a04432a5e5487bc618f49e_l3.png</center>

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**Example Three**

Substitute x = 0.5 in the expression https://quicklatex.com/cache3/af/ql_3531d56dbe9f3ee6654e4f983475f1af_l3.png.


<center>https://quicklatex.com/cache3/fe/ql_29fd15289295127df784e5b8d2c34afe_l3.png</center>

<center><img src="https://cdn.pixabay.com/photo/2016/03/03/10/20/mathematics-1233876_960_720.jpg" /></center>
<center><a href="https://cdn.pixabay.com/photo/2016/03/03/10/20/mathematics-1233876_960_720.jpg">Pixabay Image Source</a></center>

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## Harder Cases
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Evaluating algebraic expressions can get really difficult and messy. Here are some harder examples. 

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**Example One**

Substitute x = 1, y = 10 in the following expression.

<center>https://quicklatex.com/cache3/35/ql_49f6c86951d4da68e53e2b45d8ede735_l3.png</center>

**Solution**

<center>https://quicklatex.com/cache3/9a/ql_14f5494908f2a08e47245210daeb899a_l3.png</center>

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**Example Two**

Substitute x = 1, y = -1, z = 2 in the following expression.

<center>https://quicklatex.com/cache3/59/ql_b58056141a2d04545a1b8e93b21d7259_l3.png</center>

**Solution**

<center>https://quicklatex.com/cache3/7a/ql_f54e1f670306bbc9b1a535e80e3bc27a_l3.png</center>

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This solution involves a lot of negative numbers so be careful.


<center><img src="https://cdn.pixabay.com/photo/2015/11/15/07/47/mathematics-1044091_960_720.jpg" /></center>
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## Practice Problems With Solutions
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1) Find the value of 3x - 1 when x = 3.

2) Find the value of y^2 + 2y - 1 when y = -1.

3) Given the expression of xyz - 2y where x = 0.5, y = -0.5 and z = 8.

4) Find the value of the expression https://quicklatex.com/cache3/a2/ql_b104d1a46436768f858f0c3718b0d5a2_l3.png where x = 10 and y = 2. 

5) Determine the value of the expression below when x = -1, y = 2, z = 3.

<center>https://quicklatex.com/cache3/37/ql_f714c66023fd411f132fb06413cc7837_l3.png</center>


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**Solutions**

Here are the solutions to the above practice problems.

1) 8

2) -2

3) With x = 0.5, y = -0.5 and z = 8, xyz - 2y becomes -2 - 2 (-0.5) = -2 + 1 = -1

4) 10

5) Determine the value of the expression below when x = -1, y = 2, z = 3.

<center>https://quicklatex.com/cache3/37/ql_f714c66023fd411f132fb06413cc7837_l3.png</center>

**Solution**

<center>https://quicklatex.com/cache3/c9/ql_c21aeddbed2bb2d9f7acecde7474a9c9_l3.png</center>

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<center><img src="https://cdn.pixabay.com/photo/2018/11/17/12/27/mathematics-3821034_960_720.jpg" /></center>
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<center>Thank you for reading.</center>