Question

factor the following binomial.
$81x^2 - 16$
$(?x + \square)(\square x - \square)$

Explanation:

Step1: Identify the form

The binomial \(81x^2 - 16\) is a difference of squares, which has the form \(a^2 - b^2=(a + b)(a - b)\).

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

For \(81x^2\), we have \(a = 9x\) since \((9x)^2=81x^2\). For \(16\), we have \(b = 4\) since \(4^2 = 16\).

Step3: Apply the formula

Substitute \(a = 9x\) and \(b = 4\) into the difference of squares formula: \(81x^2-16=(9x + 4)(9x - 4)\).

Answer:

\((9x + 4)(9x - 4)\), so the blanks are filled as \(9\), \(4\), \(9\), \(4\) respectively.