Question

ork 15 | the quadratic form
40.b
factor each binomial.
$4x^2y^4 - 9$
answer

Explanation:

Step1: Identify the form

The binomial \(4x^{2}y^{4}-9\) is a difference of squares. Recall the difference of squares formula: \(a^{2}-b^{2}=(a + b)(a - b)\).
Here, \(a^{2}=4x^{2}y^{4}\) and \(b^{2}=9\).

Step2: Find \(a\) and \(b\)

For \(a^{2}=4x^{2}y^{4}\), take the square root: \(a=\sqrt{4x^{2}y^{4}} = 2xy^{2}\).
For \(b^{2}=9\), take the square root: \(b=\sqrt{9}=3\).

Step3: Apply the formula

Using the difference of squares formula \(a^{2}-b^{2}=(a + b)(a - b)\), substitute \(a = 2xy^{2}\) and \(b = 3\).
We get \((2xy^{2}+3)(2xy^{2}-3)\).

Answer:

\((2xy^{2}+3)(2xy^{2}-3)\)