Messin with Monomials

Hey whatz a monomial???

Monomials defined

A number like 6, 10, or 958(called a constant or a constant monomial)

A variable like x, y, or z A product ( that means multiply) of

a number and one or more variablesabc8

Polynomials Definition: the sum of monomials Special names: Binomial: is the sum of two terms xy + 3x Trinomial: is the sum of three terms a + ab + 6

Some examples of Monomials

Like Terms 7xyz, 9xyz, and

½xyz 6x, 5x, and 102x

Unlike Terms

9x and 4 y9x and 4 y

3ab, 3 bc, and 8 abc3ab, 3 bc, and 8 abc

Adding Monomials is Magic!!! When monomials

have exactly the same variables including the same exponents they are called LIKE TERMS

LIKE TERMS can be added by adding their coefficients

Monomials Added Notice that the coefficients are

added but the variable and the exponent remain the same.

222 936 xxx

More Monomials Added Be sure to compare variables and exponents before adding

coefficients They must be exactly the same If they are not LEAVE THEM ALONE

Degree

Of a variable This just means

the number of times the variable occurs as a factor in the monomial

The x is of degree 2

Of a monomial This means the

sum of the degrees of the variables

The degree of is 2 + 1 + 4 = 7

2x

425 yzx

Note The degree of any

non zero constant monomial such as 12 is 0

The Degree of a Polynomial Is the greatest of the degrees of its

terms after it has been simplified.

Monomials Multiplied To multiply these

monomials Rearrange

)4(3 22 yxxy

))()(4)(3( yyyxxx

3312 yx

Rule for Multiplying Monomials It’s easy. Just remember to

ADD the Exponents

Monomial Raised to a Power This means to

repeatedly multiply the monomial

So Means

42 )3( x

))()()()(3)(3)(3)(3( 2222 xxxx

881x

Rule for Raising Monomials to a Power

It’s easy. Just remember to

Multiply the Exponents