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Chapter 0: Problem 64

Factor using the formula for the sum or difference of two cubes. $$8 x^{3}+125$$

Short Answer

Expert verified
The factored form of the expression \(8x^3+125\) is \((2x + 5)(4x^2 - 10x + 25)\).

Step by step solution

01

Identify the cubes

First, identify if the given expression represents a sum or difference of cubes. The formula \(8x^3+125\) can be rewritten as \((2x)^3 + 5^3\). So, it is an equation that includes the sum of two cubes.
02

Apply the formula

The formula to factor the sum of cubes \(a^3 + b^3\) is \((a + b)(a^2 - ab + b^2)\). Mapping 2x to 'a' and 5 to 'b' we can apply the formula: \((2x + 5)((2x)^2 - 2x*5 + 5^2)\).
03

Simplify the expression

Now, simplify the squared and multiplications to get the factored form. This results in: \((2x + 5)(4x^2 - 10x + 25)\).

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