Factor 25x^2-20xy+3y^2

$25 x^{2} - 20 x y + 3 y^{2}$

Step 1

Factor by grouping.

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 $a \cdot c = 25 \cdot 3 = 75$ and whose sum is $b = - 20$ .

Reorder terms.

$25 x^{2} + 3 y^{2} - 20 x y$

Reorder $3 y^{2}$ and $- 20 x y$ .

$25 x^{2} - 20 x y + 3 y^{2}$

Factor $- 20$ out of $- 20 x y$ .

$25 x^{2} - 20 (x y) + 3 y^{2}$

Rewrite $- 20$ as $- 5$ plus $- 15$

$25 x^{2} + (- 5 - 15) (x y) + 3 y^{2}$

Apply the distributive property.

$25 x^{2} - 5 (x y) - 15 (x y) + 3 y^{2}$

Remove unnecessary parentheses.

$25 x^{2} - 5 x y - 15 (x y) + 3 y^{2}$

Remove unnecessary parentheses.

$25 x^{2} - 5 x y - 15 x y + 3 y^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(25 x^{2} - 5 x y) - 15 x y + 3 y^{2}$

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

$5 x (5 x - 1 y) - 3 y (5 x - y)$

Factor the polynomial by factoring out the greatest common factor, $5 x - 1 y$ .

$(5 x - 1 y) (5 x - 3 y)$

Step 2

Rewrite $- 1 y$ as $- y$ .

$(5 x - y) (5 x - 3 y)$

Factor 25x^2-20xy+3y^2

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