Problem of the Week

Updated at May 3, 2021 11:36 AM

For this week we've brought you this algebra problem.

How can we factor \(18{n}^{2}-36n+16\)?

Here are the steps:



\[18{n}^{2}-36n+16\]

1
Find the Greatest Common Factor (GCF).
GCF = \(2\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[2(\frac{18{n}^{2}}{2}+\frac{-36n}{2}+\frac{16}{2})\]

3
Simplify each term in parentheses.
\[2(9{n}^{2}-18n+8)\]

4
Split the second term in \(9{n}^{2}-18n+8\) into two terms.
\[2(9{n}^{2}-6n-12n+8)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[2(3n(3n-2)-4(3n-2))\]

6
Factor out the common term \(3n-2\).
\[2(3n-2)(3n-4)\]

Done
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