Expressions and variables

An algebraic expression comprises both numbers and variables together with at least one arithmetic operation.

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Example

$$4\cdot x-3$$

A variable, as we learned in pre-algebra, is a letter that represents unspecified numbers. One may use a variable in the same manner as all other numerals:

Addition	4+y	4 plus y
Subtraction	x-5	x minus 5
	8-a	8 minus a
Division	z/7	z divided by 7
	14/x	14 divided by x
Multiplication	9x	9 times x

To evaluate an algebraic expression you have to substitute each variable with a number and perform the operations included.

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Example

Evaluate the expression when x=5

$$4\cdot x-3$$

First we substitute x with 5

$$4\cdot 5-3$$

And then we calculate the answer

$$20-3=17$$

An expression that represents repeated multiplication of the same factor is called a power e.g.

$$5\cdot 5\cdot 5=125$$

A power can also be written as

$$5^3=125$$

Where 5 is called the base and 3 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

$$5^3=5\cdot 5\cdot 5$$

$$3^1$$	3 to the first power	$$3$$
$$4^2$$	4 to the second power or 4 squared	$$4 \cdot 4$$
$$5^3$$	5 to the third power or 5 cubed	$$5\cdot5\cdot5$$
$$2^6$$	2 to the sixth power	$$2\cdot2\cdot2\cdot2\cdot2\cdot2$$

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Evaluate the following expression when \( x = 2 \) and \( y = -3\),

\[ x^2 - y + 2x \]

\[ 10x + yx - y^2 \]

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Video lesson

Evaluate the expression when x=4 and y=3

\( 5x + y^{2}- xy \)