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Factoring the Sum & Difference of Two Cubes

Understanding how to factor the sum and difference of two perfect cubes can be straightforward with the right approach. Perfect cubes are numbers that can be expressed as the product of an integer multiplied by itself twice. For instance, 8 is a perfect cube because it equals 2 × 2 × 2. The sum and difference of cubes follow specific formulas and patterns, where recognizing signs (same or opposite) plays a key role. Mastering these concepts will enhance your algebra skills and problem-solving abilities.

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Factoring the Sum & Difference of Two Cubes

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  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. x6is x2 x2 x2 so x6 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. x6is x2 x2 x2 so x6 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.

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

  6. 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 1st term Cube root of 2nd term Product of cube root of 1st term and cube root of 2nd term.

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

  8. Try one. Cube root of 1st term Cube root of 2nd 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! Don’t forget the first rule of factoring is to look for the greatest common factor. I hope you took notes!

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