Monomials and the GCF

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A monomial is a number, a variable raised to a whole number, or a product of a number and one or more variables.

 

Examples: 12x²y,   3mn,   64w³y²

 

In algebra, a polynomial is the sum of two or more monomials.

 

Examples:   (12x²y² + 3x³y²);   (12m + 64);   and   (3p − 64p³q + 12pq²)

A polynomial with 2 terms is known as a binomial, and it's the sum of two monomials.  A polynomial with 3 terms is known as a trinomial, and so on.

 

 

 

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Factoring Monomials

To factor a monomial means to write the monomial as a product of its factors.

Finding the greatest common factor (GCF)

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Power of a Power Property

To raise a monomial to a power, multiply exponents for each variable by the external power; and raise each numeric factor to the external power.

Example:

Simplify:  (2t ⁴p³)⁴

 

 

 

 

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Answers

 

1.)  27x⁷

2.)  x⁶

3.)  81x¹²

4.)  4mn³

5.)  8x³y²