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Chapter 0: Problem 59

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

Short Answer

Expert verified
Hence, the factored form of \(x^3 + 64\) is \((x + 4)(x^2 - 4x + 16)\).

Step by step solution

01

Identify a and b

In the expression \(x^3 + 64\), it can be seen that \(a = x\) and \(b = 4\), because \(64\) is the cube of \(4\). Therefore, the given expression can be rewritten as \(x^3 + 4^3\).
02

Apply the Sum of Cubes Formula

Substitute \(a = x\) and \(b = 4\) into the sum of cubes formula, which is \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\). This gives us \((x + 4)(x^2 - 4x + 16)\).

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