Factor 7z*(2x-y)+2x-y

$7 z \cdot (2 x - y) + 2 x - y$

Step 1

Apply the distributive property.

$7 z (2 x) + 7 z (- y) + 2 x - y$

Step 2

Rewrite using the commutative property of multiplication.

$7 \cdot 2 z x + 7 z (- y) + 2 x - y$

Step 3

Rewrite using the commutative property of multiplication.

$7 \cdot 2 z x + 7 \cdot - 1 z y + 2 x - y$

Step 4

Simplify each term.

Multiply $7$ by $2$ .

$14 z x + 7 \cdot - 1 z y + 2 x - y$

Multiply $7$ by $- 1$ .

$14 z x - 7 z y + 2 x - y$

Step 5

Rewrite $14 z x - 7 z y + 2 x - y$ in a factored form.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 z x - 7 z y) + 2 x - y$

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

$7 z (2 x - y) + 1 (2 x - y)$

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

$(2 x - y) (7 z + 1)$