**Basics**

An unknown quantity is called a **variable**. A variable is usually denoted by a designated letter, such as \(x\), \(y\) , \(a\) , \(b\) and \(p\).

Example If you are given a term \(9x^2 + 6x + 3\),

\(x\) is the variable

9 is the

**coefficient**of \(x^2\)

6 is the coefficient of \(x\)

3 is the

**constant**.

A constant refers to a number that does not change. It is not a variable.

For the term \(12p^3 + 2q + 7\),
what is the constant?

**CORRECT!**

**WRONG! TRY AGAIN!**A number in front of a variable is a coefficient, not a constant.

**WRONG! TRY AGAIN!**These are variables.

**Simplifying By Like-Terms**

First, simplify according to like-terms. See if you can simplify variables, coefficients, or constants. Look for common factors.Example Simplify \(3z+7z\).

*Solution*\(3z+7z=(3+7)z=10z\)

Example Simplify \(10p-5q\).

*Solution*\(10p-5q=(5)(2p-q)\)

Simplify \(6y + 4y + y\).

Simplify \(7p + 21q\).

Need more practice? Click here to do some math drill on this topic!

Simplify \(7p + 21q\).

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When you see fractions, look for common factors in denominators and numerators, and factor out like terms!

Example Simplify \(\dfrac{4y^2+4x+8}{12}\).

*Solution*\(\require{cancel} \dfrac{4y^2+4x+8}{12} \\ \, \\ =\dfrac{4(y^2+x+2)}{12} \\ \, \\ =\dfrac{\cancel{{\color{red}{4}}}(y^2+x+2)}{\cancelto{3}{{\color{red}{12}}}} \\ \, \\ =\dfrac{y^2+x+2}{3}\)

Example Simplify \(\dfrac{7y+14z}{y+2z}\).

*Solution*\(\require{cancel} \dfrac{7y+14z}{y+2z} \\ \, \\ =\dfrac{7(y+2z)}{y+2z} \\ \, \\ =\dfrac{7\cancel{({\color{red}{y+2z}})}}{\cancel{{\color{red}{y+2z}}}} \\ \, \\ =7 \)

Simplify \(\dfrac{6x^2+9x+6}{3}\).

Need more practice? Click here to do some math drill on this topic!

Need more practice? Click here to do some math drill on this topic!

**Using The Properties of 1**

Multiplying or dividing by 1 DOES NOT change the equation. Using this property, we can use the same denominator and numerator that is equal to 1 to simplify.Example Simplify \(\dfrac{6x+3}{\sqrt{3}}\).

*Solution*\(\require{cancel} \dfrac{6x+3}{\sqrt{3}} \\ \, \\ =\dfrac{3(2x+1)}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}} \\ \, \\ =\dfrac{3\sqrt{3}(2x+1)}{3} \\ \, \\ =\dfrac{\cancel{{\color{red}{3}}}\sqrt{3}(2x+1)}{\cancel{{\color{red}{3}}}} \\ \, \\ =\sqrt{3}(2x+1) \)

Simplify \(\dfrac{2x+4}{\sqrt{2}}\).

Need more practice? Click here to do some math drill on this topic!

Need more practice? Click here to do some math drill on this topic!

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