Question

question 8 of 10
the expression below is a sum of cubes.
125x³ + 144

a. true
b. false

Explanation:

Step1: Recall sum of cubes formula

A sum of cubes is in the form \(a^3 + b^3\), where \(a\) and \(b\) are real numbers.

Step2: Analyze \(125x^3\)

We can rewrite \(125x^3\) as \((5x)^3\), since \(5^3 = 125\) and \((x)^3=x^3\), so \(a = 5x\) here.

Step3: Analyze \(144\)

Now, we check if \(144\) is a perfect cube. The cube of \(5\) is \(125\) (\(5^3=125\)) and the cube of \(6\) is \(216\) (\(6^3 = 216\)). Since \(144\) is between \(5^3\) and \(6^3\) and not equal to any integer's cube, it cannot be written as \(b^3\) where \(b\) is an integer (or a real number in the context of simple cubic terms here). So \(125x^3+144\) is not in the form \(a^3 + b^3\) because \(144\) is not a perfect cube.

Answer:

B. False