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How to factor Sum of Cubes
Formula for Sum of cubes and their factors
The general formula for the factors of the sum of cubes is
a3 + b3 = (a + b)(a² – ab + b²)
How to Factor the Sum of Cubes
To understand the how to factor the sum of cubes, let's first mutliply the factors to see how we arrive at a sum of cubes like x3 + 33
- Let's multiply the binomial (x + 3) by the trinomial (x² – 3x + 3²)
Notice that (x + 3) (x² – 3x + 3²) assumes the same pattern as the general formula for the factors of the sum of cubes. What we are going to see is that when we mutliply these two factors, several terms will cancel out and we will arrive at a final product of x3 + 27, which is exactly what the formula states
- (x + 3)(x² – 3x + 9)
- x3 – 3x² + 9x
- + 3x² – 9x + 27
- x3 – 3x²+3x² + 9x – 9x + 27 (Notice the terms that cancel out)
- x3 + 27
- x3+ 27 = x3 + 3 3
- x 3 + 3 3 = (x + 3)(x² – 3x + 3²)
How to factor the difference of cubes
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