Factor x^2+12xy+35y^2

$x^{2} + 12 x y + 35 y^{2}$

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 $a \cdot c = 1 \cdot 35 = 35$ and whose sum is $b = 12$ .

Reorder terms.

$x^{2} + 35 y^{2} + 12 x y$

Reorder $35 y^{2}$ and $12 x y$ .

$x^{2} + 12 x y + 35 y^{2}$

Factor $12$ out of $12 x y$ .

$x^{2} + 12 (x y) + 35 y^{2}$

Rewrite $12$ as $5$ plus $7$

$x^{2} + (5 + 7) (x y) + 35 y^{2}$

Apply the distributive property.

$x^{2} + 5 (x y) + 7 (x y) + 35 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 5 x y + 7 (x y) + 35 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 5 x y + 7 x y + 35 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} + 5 x y) + 7 x y + 35 y^{2}$

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

$x (x + 5 y) + 7 y (x + 5 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x + 5 y$ .

$(x + 5 y) (x + 7 y)$

Factor x^2+12xy+35y^2

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