Question

question
factor completely:
$4x^2(x^2 + 4) - 3(x^2 + 4)$

Explanation:

Step1: Identify common factor

Both terms have a common factor of \((x^2 + 4)\). Factor it out:
\((x^2 + 4)(4x^2 - 3)\)

Step2: Check for further factoring

The quadratic \(4x^2 - 3\) can be factored as a difference of squares (since \(4x^2=(2x)^2\) and \(3 = (\sqrt{3})^2\)):
\(4x^2 - 3=(2x + \sqrt{3})(2x - \sqrt{3})\)

Step3: Combine all factors

Putting it all together, the completely factored form is:
\((x^2 + 4)(2x + \sqrt{3})(2x - \sqrt{3})\)

Answer:

\((x^2 + 4)(2x + \sqrt{3})(2x - \sqrt{3})\)