Factor a^12-b^3

Problem

a^12−b^3

Solution

1. Identify the expression as a difference of cubes, which follows the pattern x^3−y^3=(x−y)*(x^2+x*y+y^2)

2. Rewrite the first term a^12 as a cube by applying the power of a power rule, such that a^12=(a^4)^3

3. Assign the variables for the formula where x=a^4 and y=b

4. Substitute these values into the difference of cubes formula.

5. Simplify the terms within the second factor by calculating (a^4)^2=a^8

Final Answer

a^12−b^3=(a^4−b)*(a^8+a^4*b+b^2)

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