Problem of the Week

Updated at Jun 3, 2024 5:50 PM

This week's problem comes from the algebra category.

How can we compute the factors of \(8{w}^{2}-24w+18\)?

Let's begin!



\[8{w}^{2}-24w+18\]

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.)
\[2(\frac{8{w}^{2}}{2}+\frac{-24w}{2}+\frac{18}{2})\]

3
Simplify each term in parentheses.
\[2(4{w}^{2}-12w+9)\]

4
Rewrite \(4{w}^{2}-12w+9\) in the form \({a}^{2}-2ab+{b}^{2}\), where \(a=2w\) and \(b=3\).
\[2({(2w)}^{2}-2(2w)(3)+{3}^{2})\]

5
Use Square of Difference: \({(a-b)}^{2}={a}^{2}-2ab+{b}^{2}\).
\[2{(2w-3)}^{2}\]

Done
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