Factor x^3-343

Problem

x^3−343

Solution

1. Identify the expression as a difference of cubes, which follows the form a^3−b^3

2. Determine the values of a and b by taking the cube root of each term.

3. Calculate the cube root of x^3 which is x so a=x

4. Calculate the cube root of 343 which is 7 (since 7×7×7=343, so b=7

5. Apply the formula for the difference of cubes: a^3−b^3=(a−b)*(a^2+a*b+b^2)

6. Substitute a=x and b=7 into the formula.

7. Simplify the terms inside the second factor: x^2+(x)*(7)+7^2 becomes x^2+7*x+49

Final Answer

x^3−343=(x−7)*(x^2+7*x+49)

Want more problems? Check here!