Question

factor the polynomial. drag the expressions into the box if they are part of the factored form of the polynomial. $b^4 - 16$

Explanation:

Step1: Recognize as difference of squares

The polynomial \(b^4 - 16\) can be written as \((b^2)^2 - 4^2\), which is a difference of squares. The formula for difference of squares is \(a^2 - b^2=(a + b)(a - b)\). So, \( (b^2)^2 - 4^2=(b^2 + 4)(b^2 - 4)\).

Step2: Factor \(b^2 - 4\) further

Notice that \(b^2 - 4\) is also a difference of squares, with \(a = b\) and \(b = 2\). Using the difference of squares formula again, \(b^2 - 4=(b + 2)(b - 2)\).

Step3: Combine the factors

Putting it all together, the factored form of \(b^4 - 16\) is \((b^2 + 4)(b + 2)(b - 2)\).

Answer:

\((b^2 + 4)(b + 2)(b - 2)\)