Factor x^2+14xy+24y^2

$x^{2} + 14 x y + 24 y^{2}$

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 $a \cdot c = 1 \cdot 24 = 24$ and whose sum is $b = 14$ .

Reorder terms.

$x^{2} + 24 y^{2} + 14 x y$

Reorder $24 y^{2}$ and $14 x y$ .

$x^{2} + 14 x y + 24 y^{2}$

Factor $14$ out of $14 x y$ .

$x^{2} + 14 (x y) + 24 y^{2}$

Rewrite $14$ as $2$ plus $12$

$x^{2} + (2 + 12) (x y) + 24 y^{2}$

Apply the distributive property.

$x^{2} + 2 (x y) + 12 (x y) + 24 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 2 x y + 12 (x y) + 24 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 2 x y + 12 x y + 24 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} + 2 x y) + 12 x y + 24 y^{2}$

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

$x (x + 2 y) + 12 y (x + 2 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x + 2 y$ .

$(x + 2 y) (x + 12 y)$

Factor x^2+14xy+24y^2

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