Question

1. $36x^4 - 100$

Explanation:

Step1: Factor out the greatest common factor (GCF)

The GCF of \(36x^4\) and \(100\) is \(4\). So we factor out \(4\):
\(36x^4 - 100 = 4(9x^4 - 25)\)

Step2: Recognize the difference of squares

Notice that \(9x^4=(3x^2)^2\) and \(25 = 5^2\), so \(9x^4 - 25\) is a difference of squares, which can be factored as \((a^2 - b^2)=(a - b)(a + b)\) where \(a = 3x^2\) and \(b = 5\):
\(9x^4 - 25=(3x^2 - 5)(3x^2 + 5)\)

Step3: Combine the factors

Putting it all together, we have:
\(36x^4 - 100 = 4(3x^2 - 5)(3x^2 + 5)\)

Answer:

\(4(3x^2 - 5)(3x^2 + 5)\)