Factor x^3+64

Problem

x3+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 a3+b3 by recognizing that 64=4

x3+4

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=4 into the formula.

(x+4)*(x2−(x)*(4)+4)

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

(x+4)*(x2−4*x+16)

Final Answer

x3+64=(x+4)*(x2−4*x+16)

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