Factor x^3+64

Problem

x^3+64

Solution

1. Identify the expression as a sum of two cubes, since both terms can be written as quantities raised to the third power.

2. Rewrite the terms in the form a^3+b^3 by recognizing that 64=4^3

x^3+4^3

3. Apply the formula for the sum of cubes, which is a^3+b^3=(a+b)*(a^2−a*b+b^2)

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

(x+4)*(x^2−(x)*(4)+4^2)

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

(x+4)*(x^2−4*x+16)

Final Answer

x^3+64=(x+4)*(x^2−4*x+16)

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