Monomials

**Monomials and the GCF**

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

Examples: 12x^{2}y, 3mn, 64w^{3}y^{2}

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

Examples: (12x^{2}y^{2}+3x^{3}y^{2});(12m+ 64); and (3p− 64p^{3}q+ 12pq^{2})

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.

**Factoring Monomials**

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

**Finding the greatest common factor (GCF)**

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^{4}p^{3})^{4}

**Practice**

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Simplify the following monomials.

Find the GCF for the following.

Answers

1.) 27x

^{7}2.) x

^{6}3.) 81x

^{12}4.) 4mn

^{3}5.) 8x

^{3}y^{2}