Factor x^2+6xy+5y^2

$x^{2} + 6 x y + 5 y^{2}$

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 $a \cdot c = 1 \cdot 5 = 5$ and whose sum is $b = 6$ .

Reorder terms.

$x^{2} + 5 y^{2} + 6 x y$

Reorder $5 y^{2}$ and $6 x y$ .

$x^{2} + 6 x y + 5 y^{2}$

Factor $6$ out of $6 x y$ .

$x^{2} + 6 (x y) + 5 y^{2}$

Rewrite $6$ as $1$ plus $5$

$x^{2} + (1 + 5) (x y) + 5 y^{2}$

Apply the distributive property.

$x^{2} + 1 (x y) + 5 (x y) + 5 y^{2}$

Multiply $x y$ by $1$ .

$x^{2} + x y + 5 (x y) + 5 y^{2}$

Remove unnecessary parentheses.

$x^{2} + x y + 5 x y + 5 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} + x y) + 5 x y + 5 y^{2}$

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

$x (x + y) + 5 y (x + y)$

Step 3

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

$(x + y) (x + 5 y)$

Factor x^2+6xy+5y^2

Related Questions

Support LCMGCF.com by disabling your adblocker.