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y^{2}\left(y-5\right)-4\left(y-5\right)
Do the grouping y^{3}-5y^{2}-4y+20=\left(y^{3}-5y^{2}\right)+\left(-4y+20\right), and factor out y^{2} in the first and -4 in the second group.
\left(y-5\right)\left(y^{2}-4\right)
Factor out common term y-5 by using distributive property.
\left(y-2\right)\left(y+2\right)
Consider y^{2}-4. Rewrite y^{2}-4 as y^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(y-5\right)\left(y-2\right)\left(y+2\right)
Rewrite the complete factored expression.