How do you factor cubes?


Quick Answer

To factor cubes, rewrite the original problem as two perfect cubes, square-multiply-square that answer and then write the final answer. If there is a greatest common factor in the original problem, factor that out. Be sure to include it in the final answer.

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Full Answer

Factoring a problem into a sum of cubes only takes a few steps. Multiplication is the main skill needed to find the answer.

Step 1: Write the original problem as two perfect cubes

Using the problem x3+64, this step is (x)3+(4)3. To make for easy reference for the rest of the process, simply use x + 4 and disregard the square for now.

Step 2: Square-multiply-square

  • Using the answer from Step 1, in this case x + 4, square the first item in the problem. This gives the answer x2.
  • Next, multiply the two items in the problem; in this case the answer is 4x.
  • Finally, square the last item in the problem, giving the answer of 16.

Step 3: Write the final answer

Factoring cubes always results in two sets of equations. To write the answer, first write the equation from Step 1, in this case (x + 4). Next, write an equation using the terms from Step 2. For this problem, use x2, 4x and 16. It is important that the plus and minus signs are correct. The second sign is the opposite of the one in the original problem and always ends with a plus sign. This answer is x2 - 4x + 16. The final answer is (x+4) (x2 - 4x + 16).

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