Algebra Vocabulary

Variable-  a letter that stands for a number:  x, y, a, c…

What x stand for in one problem will be different from what x stands for in another problem.  It varies, so it is called a variable.

Coefficient-  the number that comes before the variable.  The coefficient and the variable are being multiplied.  3a means 3 times a or 3 a’s (like 3 apples)

If no coefficient is written, the coefficient is 1.

Examples:  7yz (7 is the coefficient), 135q (135 is the coefficient), a (1 is the coefficient)

Constant-  a regular number (no variable attached to it), Ex:  5, 3/5, -11

Constants do not change how much they are worth from problem to problem like variables do.  They are constantly the same, so they are called constants.

Exponent-  the little number to the top right of a constant or variable, squared, cubed, 4^th power, etc.

If no exponent is written, the exponent is 1.

Examples:  6²  is 6 squared, 2 is the exponent, it means 6 times 6

                   z⁵ is z to the 5^th power, 5 is the exponent, it means z times z times z times z times z

                   y, since no exponent is written, the exponent is 1.

Like terms-  must have the exact same variables and exponents, they can have different coefficients

Examples:  -9xy is a like term with ½xy,   4a & 23a are like terms, y³ & -96y³ are like terms

Constants are all like terms with each other:  45, -99, 8743, 7/9, etc.

These are not like terms:  2y and 4y² because the y’s do not have the same exponent

In some books, like terms are called similar terms.

Like terms can be added or subtracted.

Unlike terms cannot be added or subtracted.

Examples;

-7yz² + 2yz²= -5yz²  The coefficients are added and the variable part stays the same.

2x – 8xy= can’t be done because they aren’t like terms, their variable parts are different

You do not need like terms to multiply or divide!

(7y)(-6b)= -42by 

You multiply the coefficients and put the variables together.

(8x)(4x)(2)= 64x²

You multiply the coefficients and the constant, then since they both have the same variable, you add the exponents.

9x/3= 3x

You divide the coefficient by the constant in the denominator and the variable stays the same.

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