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 8w2−24w+188{w}^{2}-24w+18?

Let's begin!



8w2−24w+188{w}^{2}-24w+18

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(8w22+−24w2+182)2(\frac{8{w}^{2}}{2}+\frac{-24w}{2}+\frac{18}{2})

3
Simplify each term in parentheses.
2(4w2−12w+9)2(4{w}^{2}-12w+9)

4
Rewrite 4w2−12w+94{w}^{2}-12w+9 in the form a2−2ab+b2{a}^{2}-2ab+{b}^{2}, where a=2wa=2w and b=3b=3.
2((2w)2−2(2w)(3)+32)2({(2w)}^{2}-2(2w)(3)+{3}^{2})

5
Use Square of Difference: (a−b)2=a2−2ab+b2{(a-b)}^{2}={a}^{2}-2ab+{b}^{2}.
2(2w−3)22{(2w-3)}^{2}

Done
Cymath foriOSAndroid