Question

factor completely.
$100x^2 - 4x^4$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of \(100x^2\) and \(4x^4\). The GCF of 100 and 4 is 4, and the GCF of \(x^2\) and \(x^4\) is \(x^2\). So we factor out \(4x^2\):
\(100x^2 - 4x^4 = 4x^2(25 - x^2)\)

Step2: Factor the difference of squares

Notice that \(25 - x^2\) is a difference of squares, which can be factored as \(a^2 - b^2=(a + b)(a - b)\), where \(a = 5\) and \(b = x\):
\(25 - x^2=(5 + x)(5 - x)\)

Step3: Combine the factors

Putting it all together, the completely factored form is:
\(4x^2(5 + x)(5 - x)\)

Answer:

\(4x^2(5 + x)(5 - x)\)