# 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).1 What is the largest number that divides evenly into $$18{n}^{2}$$, $$-36n$$, and $$16$$?It is $$2$$.2 What is the highest degree of $$n$$ that divides evenly into $$18{n}^{2}$$, $$-36n$$, and $$16$$?It is 1, since $$n$$ is not in every term.3 Multiplying the results above,The GCF is $$2$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!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.1 Multiply the coefficient of the first term by the constant term.$9\times 8=72$2 Ask: Which two numbers add up to $$-18$$ and multiply to $$72$$?$$-6$$ and $$-12$$3 Split $$-18n$$ as the sum of $$-6n$$ and $$-12n$$.$9{n}^{2}-6n-12n+8$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$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 $$3n-2$$.$2(3n-2)(3n-4)$Done2*(3*n-2)*(3*n-4)