Factor 4x^2+13xy+10y^2

$4 x^{2} + 13 x y + 10 y^{2}$

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 $a \cdot c = 4 \cdot 10 = 40$ and whose sum is $b = 13$ .

Reorder terms.

$4 x^{2} + 10 y^{2} + 13 x y$

Reorder $10 y^{2}$ and $13 x y$ .

$4 x^{2} + 13 x y + 10 y^{2}$

Factor $13$ out of $13 x y$ .

$4 x^{2} + 13 (x y) + 10 y^{2}$

Rewrite $13$ as $5$ plus $8$

$4 x^{2} + (5 + 8) (x y) + 10 y^{2}$

Apply the distributive property.

$4 x^{2} + 5 (x y) + 8 (x y) + 10 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} + 5 x y + 8 (x y) + 10 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} + 5 x y + 8 x y + 10 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 5 x y) + 8 x y + 10 y^{2}$

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

$x (4 x + 5 y) + 2 y (4 x + 5 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 5 y$ .

$(4 x + 5 y) (x + 2 y)$

Factor 4x^2+13xy+10y^2

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