Problem 80 - Introductory Algebra for College Students

Question

Factor using the formula for the sum or difference of two cubes. $$x^{3}+64$$

Step-by-Step Solution

Answer

The factored form of \(x^3 + 64\) is \((x + 4)(x^2 - 4x + 16)\)

Step 1: Write the Expression in the Form of Sum of Cubes

Recognize that x^3 + 64 can be written as x^3 + 4^3 where a = x and b = 4

Step 2: Apply the Formula

Substitute a = x, b = 4 in the formula for the sum of cubes, which is (a + b)(a^2 - ab + b^2). The expression x^3 + 4^3 becomes (x + 4)(x^2 - 4x + 16)

Step 3: Final Result

At last, the factored form of x^3 + 64 is (x + 4)(x^2 - 4x + 16)