Question

$x^4 - x^2$

Explanation:

Step1: Factor out the common term

We can factor out \(x^{2}\) from the expression \(x^{4}-x^{2}\) because both terms have \(x^{2}\) as a factor. Using the distributive property \(ab - ac=a(b - c)\), where \(a = x^{2}\), \(b=x^{2}\), and \(c = 1\), we get:
\(x^{4}-x^{2}=x^{2}(x^{2}-1)\)

Step2: Factor the difference of squares

The term \(x^{2}-1\) is a difference of squares, which can be factored using the formula \(a^{2}-b^{2}=(a + b)(a - b)\). Here, \(a=x\) and \(b = 1\), so:
\(x^{2}-1=(x + 1)(x - 1)\)

Step3: Combine the factors

Substituting the factored form of \(x^{2}-1\) back into the expression from Step 1, we have:
\(x^{4}-x^{2}=x^{2}(x + 1)(x - 1)\)

Answer:

\(x^{2}(x + 1)(x - 1)\) (or the original factoring steps can also be considered as simplifying the expression, and the fully factored form is \(x^{2}(x + 1)(x - 1)\))