### Algebra: Variables

### Simplification

SimplificationFor #4 \cdot 5 x# we can also write #20x#.

Hence, we can write #4 \cdot 5 x# in a more simplified manner. We can call this **simplifying **an expression.

**Example**

\[\begin{array}{rcl}

{\blue{5\cdot 8} x} &{=}& {\blue{40}x}

\end{array}\]

The product #\blue x\cdot \green y# is the same as #\green y\cdot \blue x#. |
\[\begin{array}{rcl} {3 \cdot \green{y} \cdot 6 \cdot \blue{x}} &{=}&{3 \cdot {6} \cdot {\blue{x}} \cdot {\green{y}}} \\&{=}&{{\purple{18}} {\blue{x}} {\green{y}}} \end{array}\] |

The sum #3\blue{x} + 2\blue{x}# has similar terms. Similar terms can be simplified by combining the similar terms together. To combine like terms, we add the coefficients. |

#19xy#

#\begin{array}{rcl}

10xy+9xy &= &19xy\\

&&\blue{\text{coefficients \(10\) and \(9\) of \(xy\) added}}

\end{array}#

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