Factoring the Sum Difference of Two Cubes This

Factoring the Sum & Difference of Two Cubes

This is a piece of cake, if you have perfect cubes. What are perfect cubes?

This is a piece of cake, if you have perfect cubes. What are perfect cubes? Something times something. Where the something is a factor 3 times. 8 is 2 2 2, so 8 is a perfect cube. x 6 is x 2 so x 6 is a perfect cube. It is easy to see if a variable is a perfect cube, how?

This is a piece of cake, if you have perfect cubes. What are perfect cubes? Something times something. Where the something is a factor 3 times. 8 is 2 2 2, so 8 is a perfect cube. x 6 is x 2 so x 6 is a perfect cube. It is easy to see if a variable is a perfect cube, how? See if the exponent is divisible by 3. It’s harder for integers.

The sum or difference of two cubes will factor into a binomial trinomial. same sign always opposite always +

Now we know how to get the signs, let’s work on what goes inside. Square this term to get this term. Cube root of 1 st term Cube root of 2 nd term Product of cube root of 1 st term and cube root of 2 nd term.

Try one. Make a binomial and a trinomial with the correct signs.

Try one. Cube root of 1 st term Cube root of 2 nd term

Try one. Square this term to get this term.

Try one. Multiply 3 x an 5 to get this term.

Try one. Square this term to get this term.

Try one. You did it! Don’t forget the first rule of factoring is to look for the greatest common factor. I hope you took notes!