Factor 8x^2+11xy+3y^2

$8 x^{2} + 11 x y + 3 y^{2}$

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 $a \cdot c = 8 \cdot 3 = 24$ and whose sum is $b = 11$ .

Reorder terms.

$8 x^{2} + 3 y^{2} + 11 x y$

Reorder $3 y^{2}$ and $11 x y$ .

$8 x^{2} + 11 x y + 3 y^{2}$

Factor $11$ out of $11 x y$ .

$8 x^{2} + 11 (x y) + 3 y^{2}$

Rewrite $11$ as $3$ plus $8$

$8 x^{2} + (3 + 8) (x y) + 3 y^{2}$

Apply the distributive property.

$8 x^{2} + 3 (x y) + 8 (x y) + 3 y^{2}$

Remove unnecessary parentheses.

$8 x^{2} + 3 x y + 8 (x y) + 3 y^{2}$

Remove unnecessary parentheses.

$8 x^{2} + 3 x y + 8 x y + 3 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} + 3 x y) + 8 x y + 3 y^{2}$

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

$x (8 x + 3 y) + y (8 x + 3 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $8 x + 3 y$ .

$(8 x + 3 y) (x + y)$

Factor 8x^2+11xy+3y^2

Related Questions

Support LCMGCF.com by disabling your adblocker.