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Factoring the Sum & Difference of Two Cubes. This is a piece of cake, if you have perfect cubes. What are perfect cubes?

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Presentation on theme: "Factoring the Sum & Difference of Two Cubes. This is a piece of cake, if you have perfect cubes. What are perfect cubes?"— Presentation transcript:

1 Factoring the Sum & Difference of Two Cubes

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

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

4 This is a piece of cake, if you have perfect cubes. What are perfect cubes? Something times 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 x 2 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. Its harder for integers.

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

6 Now we know how to get the signs, lets work on what goes inside. 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. Square this term to get this term.

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

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

9 Try one. Square this term to get this term.

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

11 Try one. Square this term to get this term.

12 Try one. You did it! Dont forget the first rule of factoring is to look for the greatest common factor. I hope you took notes!


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