Today in class we learned about how to find he GCF of a variable expression and how to simplify and make equivalent Algebraic Fractions:

GCF in a Variable Expression:

First, you must find the prime factorization of the coefficient. Then write the variable in expanded form. Next , all you have to do is find common factors. It's that simple!

Examples:

8xy² and 6x³y

2*2*2*x*y*y 2*3*x*x*x*y

So, the GCF of 8x² and 6x³y is 2xy

Note: When finding the GCF of a variable expression always list the numbers in numerical order then the letters in alphabetical order.

You can also use a Venn Diagram to find the GCF:

8xy^{2 6x3 y}

2*2*2*x*y*y 2*3*x*x*x*y

Their similarities(which are underlined) would go in the middle.

Algebraic Factions:

To write Algebraic Fractions in simplest form, first write the prime factorization of the expression.

Then, divide the numerator and denominator by the common factors.

Example:

4ab^{2 2*2*a*b*b = b2}

16ac 2*2*2*2*a*c = 4c