# Factor the polynomial if it is a perfect square trinomial,

Factor the polynomial if it is a perfect square trinomial, or state that the polynomial is prime.
${x}^{2}+18xy+81{y}^{2}$
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Step 1
The polynomial is given as , ${x}^{2}+18xy+81{y}^{2}$.
Factorization of the polynomial,
${x}^{2}+18xy+81{y}^{2}={x}^{2}+18xy+{\left(9y\right)}^{2}$
$={\left(x+9y\right)}^{2}$
=(x+9y)(x+9y)
Step 2
The factors of the polynomial ${x}^{2}+18xy+81{y}^{2}$ is ${\left(x+9y\right)}^{2}$.
The factors are not the prime , as the prime numbers multiplied together does not give the prime factor.
Hence the polynomial is not a prime.