Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Multiply $- 2$ by $- 2$ .

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

Step 3

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

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Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

Step 4

Simplify each term.

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Step 4.1

Rewrite using the commutative property of multiplication.

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

Step 4.2

Multiply $2$ by $- 1$ .

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

Step 4.3

Rewrite using the commutative property of multiplication.

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

Step 4.4

Multiply $- 1$ by $- 1$ .

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

Step 4.5

Multiply $a$ by $1$ .

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

Step 5

Subtract $a x$ from $a x$ .

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

Step 6

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

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

Step 7

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

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

Step 8

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

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

Step 9

Add $- a y$ and $0$ .

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

Step 10

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

$- a y + 2 b y$

Step 11

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

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Step 11.1

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

$- y (a) + 2 b y$

Step 11.2

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

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

Step 11.3

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

$- y (a - 2 b)$