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.
Continue ReadingFactoring 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 x^{3}+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
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 x^{2}, 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 x^{2} - 4x + 16. The final answer is (x+4) (x^{2} - 4x + 16).
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