Question

factor the polynomial. drag the expressions into the box if they are part of the factored form of the polynomial.
$a^2 - 196$

Explanation:

Step1: Identify the form

The polynomial \(a^2 - 196\) is a difference of squares. The formula for factoring a difference of squares is \(x^2 - y^2=(x + y)(x - y)\).
Here, \(x = a\) and \(y^2=196\), so we find \(y\) by taking the square root of 196.

Step2: Find the square root of 196

\(\sqrt{196} = 14\), so \(y = 14\).

Step3: Apply the difference of squares formula

Substitute \(x = a\) and \(y = 14\) into the formula \(x^2 - y^2=(x + y)(x - y)\).
We get \(a^2-196=(a + 14)(a - 14)\).

Answer:

\((a + 14)(a - 14)\)