Factor trinomial, or state that the trinomial is prime: 3x2+4xy+y2

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Step 1
We have to factor the trinomial or state that the trinomial is prime:

3 x^{2} + 4 x y + y^{2}

Factorization is the process of taking common and that common parts are known as factor of that expression.
Factorizing the trinomial by middle term splitting method,
In middle term splitting method first we multiply first and last term constant coefficients then we do prime factor of that multiplied part and after adding or subtracting we substitute the middle term.
Here first and last term constant coefficient are 3 and 1 respectively
Therefore,

3 \times 1

So for middle term 4,
3+1=4
Step 2
Now factorizing the trinomial by using middle term splitting method,

3 x^{2} + 4 x y + y^{2} = 3 x^{2} + 3 x y + x y + y^{2}

=3x(x+y)+y(x+y)
=(x+y)(3x+y)
Hence, factorization of the trinomial is (x+y)(3x+y).
Note:
If it was not factorable then it could be prime.

Factor trinomial, or state that the trinomial is prime: 3x^{2}+4xy+y^{2}

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