Factor 64x^3+27

Problem

64*x3+27

Solution

1. Identify the expression as a sum of two cubes, which follows the form a3+b3

2. Determine the cube roots of each term to find a and b

3. Calculate a by taking the cube root of 64*x3 which results in a=4*x

4. Calculate b by taking the cube root of 27 which results in b=3

5. Apply the formula for the sum of cubes: a3+b3=(a+b)*(a2−a*b+b2)

6. Substitute the values of a and b into the formula.

7. Simplify the terms within the second factor: (4*x)2=16*x2 (4*x)*(3)=12*x and 3=9

Final Answer

64*x3+27=(4*x+3)*(16*x2−12*x+9)

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