Factor 4x^2+7xy+3y^2

$4 x^{2} + 7 x y + 3 y^{2}$

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 $a \cdot c = 4 \cdot 3 = 12$ and whose sum is $b = 7$ .

Reorder terms.

$4 x^{2} + 3 y^{2} + 7 x y$

Reorder $3 y^{2}$ and $7 x y$ .

$4 x^{2} + 7 x y + 3 y^{2}$

Factor $7$ out of $7 x y$ .

$4 x^{2} + 7 (x y) + 3 y^{2}$

Rewrite $7$ as $3$ plus $4$

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$x (4 x + 3 y) + y (4 x + 3 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 3 y$ .

$(4 x + 3 y) (x + y)$

Factor 4x^2+7xy+3y^2

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