Question

Factor the expression. Tell which special product factoring pattern you used. $$z^{2}-25$$

Short answer

The factored form of the expression is \((z+5)(z-5)\). The special pattern used is the difference of squares.

Step-by-step solution

Identify the squares

In this expression \(z^{2}-25\), \(z^2\) is a perfect square of \(z\) and \(25\) is a perfect square of \(5\). Therefore, our \(a = z\) and \(b = 5\).

Apply the difference of squares pattern

The formula for difference of squares is \(a^2 - b^2 = (a+b)(a-b)\). If we replace \(a\) with \(z\) and \(b\) with \(5\) we get: \((z+5)(z-5)\).

Write the final factored form

Once you have applied the difference of squares pattern, your final factored form of the expression is: \((z+5)(z-5)\).