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Chapter 0: Problem 93

Factor and simplify each algebraic expression. $$x^{\frac{3}{2}}-x^{\frac{1}{2}}$$

Short Answer

Expert verified
The simplified form of the algebraic expression \(x^{\frac{3}{2}}-x^{\frac{1}{2}}\) is \(x^{\frac{1}{2}}(x - 1)\)

Step by step solution

01

Identify the Common Factor

Start by identifying the common factor in both terms. In this case, the common factor is \(x^{\frac{1}{2}}\). This is because \(x^{\frac{1}{2}}\) can multiply into each term without changing the value of the expression.
02

Factor out the Common Factor

After finding the common factor, factor it out from both terms. This means we divide each term of the expression by our common factor. In doing so, \(x^{\frac{3}{2}}\) divided by \(x^{\frac{1}{2}}\) is \(x\), and \(x^{\frac{1}{2}}\) divided by \(x^{\frac{1}{2}}\) is 1.
03

Write the Simplified Expression

The final step is to write the simplified expression. The factored form of the algebraic expression \(x^{\frac{3}{2}}-x^{\frac{1}{2}}\) is, therefore, \(x^{\frac{1}{2}}(x - 1)\).

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