Problem of the Week

Updated at Mar 24, 2025 8:33 AM

This week we have another algebra problem:

How can we factor \(36{u}^{2}-54u+18\)?

Let's start!



\[36{u}^{2}-54u+18\]

1
Find the Greatest Common Factor (GCF).
GCF = \(18\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[18(\frac{36{u}^{2}}{18}+\frac{-54u}{18}+\frac{18}{18})\]

3
Simplify each term in parentheses.
\[18(2{u}^{2}-3u+1)\]

4
Split the second term in \(2{u}^{2}-3u+1\) into two terms.
\[18(2{u}^{2}-u-2u+1)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[18(u(2u-1)-(2u-1))\]

6
Factor out the common term \(2u-1\).
\[18(2u-1)(u-1)\]

Done
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