Factor x^3+343

Problem

x3+343

Solution

1. Identify the expression as a sum of two cubes, since 343 is a perfect cube.

2. Rewrite the constant term as a cube to see the terms more clearly.

343=7

3. Apply the formula for the sum of cubes, which is a3+b3=(a+b)*(a2−a*b+b2)

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

(x+7)*(x2−(x)*(7)+7)

5. Simplify the terms inside the second set of parentheses.

(x+7)*(x2−7*x+49)

Final Answer

x3+343=(x+7)*(x2−7*x+49)

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