Factor x^2-5xy+4y^2

$x^{2} - 5 x y + 4 y^{2}$

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 $a \cdot c = 1 \cdot 4 = 4$ and whose sum is $b = - 5$ .

Reorder terms.

$x^{2} + 4 y^{2} - 5 x y$

Reorder $4 y^{2}$ and $- 5 x y$ .

$x^{2} - 5 x y + 4 y^{2}$

Factor $- 5$ out of $- 5 x y$ .

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

Rewrite $- 5$ as $- 1$ plus $- 4$

$x^{2} + (- 1 - 4) (x y) + 4 y^{2}$

Apply the distributive property.

$x^{2} - 1 (x y) - 4 (x y) + 4 y^{2}$

Remove unnecessary parentheses.

$x^{2} - 1 x y - 4 (x y) + 4 y^{2}$

Remove unnecessary parentheses.

$x^{2} - 1 x y - 4 x y + 4 y^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} - 1 x y) - 4 x y + 4 y^{2}$

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

$x (x - 1 y) - 4 y (x - y)$

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

$(x - 1 y) (x - 4 y)$

Step 2

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

$(x - y) (x - 4 y)$

Factor x^2-5xy+4y^2

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