Questions: 4x^3-4x

4x^3-4x
Transcript text: d. $4 x^{3}-4 x$
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Solution

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Solution Steps

To solve the expression \(4x^3 - 4x\), we can factor out the greatest common factor from the terms. The greatest common factor here is \(4x\). After factoring, we can simplify the expression.

Step 1: Factor the Expression

We start with the expression \(4x^3 - 4x\). To simplify it, we factor out the greatest common factor, which is \(4x\):

\[ 4x^3 - 4x = 4x(x^2 - 1) \]

Step 2: Further Factorization

The term \(x^2 - 1\) is a difference of squares, which can be factored further:

\[ x^2 - 1 = (x - 1)(x + 1) \]

Thus, we can rewrite the expression as:

\[ 4x(x^2 - 1) = 4x(x - 1)(x + 1) \]

Final Answer

The fully factored form of the expression \(4x^3 - 4x\) is:

\[ \boxed{4x(x - 1)(x + 1)} \]

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