e1s2kat26

2021-01-27

Factor the polynomial $25{t}^{2}+90t+81$

Tuthornt

$25{t}^{2}+90t+81$

We have perfect squares: $25{t}^{2}=\left(5t{\right)}^{2}$ and $81={9}^{2}$

To factor as a perfect square trinomial, take twice the product of the two terms in the binomial $5t+92\left(5t\right)\left(9\right)=90t$.

Since 90t is the middle term of the trinomial, the trinomial is a perfect square. Therefore, $25{t}^{2}+90t+81=\left(5t+9{\right)}^{2}$

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