Factor 3x^2+4xy+y^2

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

Step 1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot 1 = 3$ and whose sum is $b = 4$ .

Reorder terms.

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

Reorder $y^{2}$ and $4 x y$ .

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

Factor $4$ out of $4 x y$ .

$3 x^{2} + 4 (x y) + y^{2}$

Rewrite $4$ as $1$ plus $3$

$3 x^{2} + (1 + 3) (x y) + y^{2}$

Apply the distributive property.

$3 x^{2} + 1 (x y) + 3 (x y) + y^{2}$

Multiply $x y$ by $1$ .

$3 x^{2} + x y + 3 (x y) + y^{2}$

Remove unnecessary parentheses.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} + x y) + 3 x y + y^{2}$

Factor out the greatest common factor (GCF) from each group.

$x (3 x + y) + y (3 x + y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + y$ .

$(3 x + y) (x + y)$

Factor 3x^2+4xy+y^2

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