Factor (a-2b)(x-2y)+(2b-a)(x-y)

$(a - 2 b) (x - 2 y) + (2 b - a) (x - y)$

Expand $(a - 2 b) (x - 2 y)$ using the FOIL Method.

Apply the distributive property.

$a (x - 2 y) - 2 b (x - 2 y) + (2 b - a) (x - y)$

Apply the distributive property.

$a x + a (- 2 y) - 2 b (x - 2 y) + (2 b - a) (x - y)$

Apply the distributive property.

$a x + a (- 2 y) - 2 b x - 2 b (- 2 y) + (2 b - a) (x - y)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$a x - 2 a y - 2 b x - 2 b (- 2 y) + (2 b - a) (x - y)$

Rewrite using the commutative property of multiplication.

$a x - 2 a y - 2 b x - 2 \cdot - 2 b y + (2 b - a) (x - y)$

Multiply $- 2$ by $- 2$ .

$a x - 2 a y - 2 b x + 4 b y + (2 b - a) (x - y)$

Expand $(2 b - a) (x - y)$ using the FOIL Method.

Apply the distributive property.

$a x - 2 a y - 2 b x + 4 b y + 2 b (x - y) - a (x - y)$

Apply the distributive property.

$a x - 2 a y - 2 b x + 4 b y + 2 b x + 2 b (- y) - a (x - y)$

Apply the distributive property.

$a x - 2 a y - 2 b x + 4 b y + 2 b x + 2 b (- y) - a x - a (- y)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$a x - 2 a y - 2 b x + 4 b y + 2 b x + 2 \cdot - 1 b y - a x - a (- y)$

Multiply $2$ by $- 1$ .

$a x - 2 a y - 2 b x + 4 b y + 2 b x - 2 b y - a x - a (- y)$

Rewrite using the commutative property of multiplication.

$a x - 2 a y - 2 b x + 4 b y + 2 b x - 2 b y - a x - 1 \cdot - 1 a y$

Multiply $- 1$ by $- 1$ .

$a x - 2 a y - 2 b x + 4 b y + 2 b x - 2 b y - a x + 1 a y$

Multiply $a$ by $1$ .

$a x - 2 a y - 2 b x + 4 b y + 2 b x - 2 b y - a x + a y$

Subtract $a x$ from $a x$ .

$- 2 a y - 2 b x + 4 b y + 2 b x - 2 b y + 0 + a y$

Add $- 2 a y$ and $0$ .

$- 2 a y - 2 b x + 4 b y + 2 b x - 2 b y + a y$

Add $- 2 a y$ and $a y$ .

$- a y - 2 b x + 4 b y + 2 b x - 2 b y$

Add $- 2 b x$ and $2 b x$ .

$- a y + 4 b y + 0 - 2 b y$

Add $- a y$ and $0$ .

$- a y + 4 b y - 2 b y$

Subtract $2 b y$ from $4 b y$ .

$- a y + 2 b y$

Factor $- y$ out of $- a y + 2 b y$ .

Factor $- y$ out of $- a y$ .

$- y (a) + 2 b y$

Factor $- y$ out of $2 b y$ .

$- y (a) - y (- 2 b)$

Factor $- y$ out of $- y (a) - y (- 2 b)$ .

$- y (a - 2 b)$

Factor (a-2b)(x-2y)+(2b-a)(x-y)

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