Problem of the Week

Updated at Sep 14, 2026 8:33 AM

This week we have another algebra problem:

How can we factor \(4{z}^{2}-4\)?

Let's start!



\[4{z}^{2}-4\]

1
Find the Greatest Common Factor (GCF).
GCF = \(4\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[4(\frac{4{z}^{2}}{4}-\frac{4}{4})\]

3
Simplify each term in parentheses.
\[4({z}^{2}-1)\]

4
Rewrite \({z}^{2}-1\) in the form \({a}^{2}-{b}^{2}\), where \(a=z\) and \(b=1\).
\[4({z}^{2}-{1}^{2})\]

5
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[4(z+1)(z-1)\]

Done
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