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Definition of Variable

The properties of numbers are often written with the help of letters.

For example,we can write the commutative property of addition as a+b=b+a{a}+{b}={b}+{a}.

In this equality we can plug any numbers instead of aa and bb: 32+4573=4573+32{32}+{4573}={4573}+{32}, 350+3=3+350{350}+{3}={3}+{350} etc.

Number, that is plugged instead of a letter is called its value.

Letters, that are used in algebra, are called variables; they are called so, because we can change value of a letter.

For example, we can set a=3{a}={3}, b=5{b}={5} or a=9{a}={9}, b=4{b}={4} in equality a+b=b+a{a}+{b}={b}+{a}.

Conclusion. Letters are used to write variables. If it is not a variable (for example, number), then it is called a constant. Value of a constant can't be changed.

Usually, letters x{x} and y{y} are used for writing variables.

2×x+3−x×y+x2+(3−x)y{\color{red}{{{2}}}}{\color{blue}{{\times}}}{\color{green}{{{x}}}}{\color{blue}{{+}}}{\color{red}{{{3}}}}{\color{blue}{{-}}}{\color{green}{{{x}}}}{\color{blue}{{\times}}}{\color{green}{{{y}}}}{\color{blue}{{+}}}{{\color{green}{{{x}}}}}^{{\color{red}{{{2}}}}}{\color{blue}{{+}}}{{\left({\color{red}{{{3}}}}{\color{blue}{{-}}}{\color{green}{{{x}}}}\right)}}^{{{\color{green}{{{y}}}}}}

Constants are red, variables are green, operations are blue.