Factor 5x(x-y)-(y-x)

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

Step 1

Apply the distributive property.

$5 x \cdot x + 5 x (- y) - (y - x)$

Step 2

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$5 (x \cdot x) + 5 x (- y) - (y - x)$

Multiply $x$ by $x$ .

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

Step 3

Rewrite using the commutative property of multiplication.

$5 x^{2} + 5 \cdot - 1 x y - (y - x)$

Step 4

Multiply $5$ by $- 1$ .

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

Step 5

Apply the distributive property.

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

Step 6

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$5 x^{2} - 5 x y - y + 1 x$

Multiply $x$ by $1$ .

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

Step 7

Rewrite $5 x^{2} - 5 x y - y + x$ in a factored form.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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