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 18n2−36n+1618{n}^{2}-36n+16?

Here are the steps:



18n2−36n+1618{n}^{2}-36n+16

1
Find the Greatest Common Factor (GCF).
GCF = 22

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2(18n22+−36n2+162)2(\frac{18{n}^{2}}{2}+\frac{-36n}{2}+\frac{16}{2})

3
Simplify each term in parentheses.
2(9n2−18n+8)2(9{n}^{2}-18n+8)

4
Split the second term in 9n2−18n+89{n}^{2}-18n+8 into two terms.
2(9n2−6n−12n+8)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))2(3n(3n-2)-4(3n-2))

6
Factor out the common term 3n−23n-2.
2(3n−2)(3n−4)2(3n-2)(3n-4)

Done
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