Question

exponents and polynomials
factoring a difference of squares in one variable: advanced
factor.
$4 - 81u^2$

Explanation:

Step1: Identify difference of squares

The expression \(4 - 81u^2\) is a difference of squares. Recall the formula for factoring a difference of squares: \(a^2 - b^2=(a + b)(a - b)\). Here, \(a^2 = 4\) and \(b^2=81u^2\).

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

Solve for \(a\): \(a=\sqrt{4} = 2\). Solve for \(b\): \(b=\sqrt{81u^2}=9u\).

Step3: Apply the formula

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

Answer:

\((2 + 9u)(2 - 9u)\)