Algebra Examples

$(a - 2 b) (3 x - 5 y) + (2 b - a) (x - y)$

Step 1

Expand $(a - 2 b) (3 x - 5 y)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$a (3 x - 5 y) - 2 b (3 x - 5 y) + (2 b - a) (x - y)$

Step 1.2

Apply the distributive property.

$a (3 x) + a (- 5 y) - 2 b (3 x - 5 y) + (2 b - a) (x - y)$

Step 1.3

Apply the distributive property.

$a (3 x) + a (- 5 y) - 2 b (3 x) - 2 b (- 5 y) + (2 b - a) (x - y)$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Rewrite using the commutative property of multiplication.

$3 a x + a (- 5 y) - 2 b (3 x) - 2 b (- 5 y) + (2 b - a) (x - y)$

Step 2.2

Rewrite using the commutative property of multiplication.

$3 a x - 5 a y - 2 b (3 x) - 2 b (- 5 y) + (2 b - a) (x - y)$

Step 2.3

Rewrite using the commutative property of multiplication.

$3 a x - 5 a y - 2 \cdot 3 b x - 2 b (- 5 y) + (2 b - a) (x - y)$

Step 2.4

Multiply $- 2$ by $3$ .

$3 a x - 5 a y - 6 b x - 2 b (- 5 y) + (2 b - a) (x - y)$

Step 2.5

Rewrite using the commutative property of multiplication.

$3 a x - 5 a y - 6 b x - 2 \cdot - 5 b y + (2 b - a) (x - y)$

Step 2.6

Multiply $- 2$ by $- 5$ .

$3 a x - 5 a y - 6 b x + 10 b y + (2 b - a) (x - y)$

Step 3

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

Tap for more steps...

Step 3.1

Apply the distributive property.

$3 a x - 5 a y - 6 b x + 10 b y + 2 b (x - y) - a (x - y)$

Step 3.2

Apply the distributive property.

$3 a x - 5 a y - 6 b x + 10 b y + 2 b x + 2 b (- y) - a (x - y)$

Step 3.3

Apply the distributive property.

$3 a x - 5 a y - 6 b x + 10 b y + 2 b x + 2 b (- y) - a x - a (- y)$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Rewrite using the commutative property of multiplication.

$3 a x - 5 a y - 6 b x + 10 b y + 2 b x + 2 \cdot - 1 b y - a x - a (- y)$

Step 4.2

Multiply $2$ by $- 1$ .

$3 a x - 5 a y - 6 b x + 10 b y + 2 b x - 2 b y - a x - a (- y)$

Step 4.3

Rewrite using the commutative property of multiplication.

$3 a x - 5 a y - 6 b x + 10 b y + 2 b x - 2 b y - a x - 1 \cdot - 1 a y$

Step 4.4

Multiply $- 1$ by $- 1$ .

$3 a x - 5 a y - 6 b x + 10 b y + 2 b x - 2 b y - a x + 1 a y$

Step 4.5

Multiply $a$ by $1$ .

$3 a x - 5 a y - 6 b x + 10 b y + 2 b x - 2 b y - a x + a y$

Step 5

Subtract $a x$ from $3 a x$ .

$2 a x - 5 a y - 6 b x + 10 b y + 2 b x - 2 b y + a y$

Step 6

Add $- 5 a y$ and $a y$ .

$2 a x - 4 a y - 6 b x + 10 b y + 2 b x - 2 b y$

Step 7

Add $- 6 b x$ and $2 b x$ .

$2 a x - 4 a y - 4 b x + 10 b y - 2 b y$

Step 8

Subtract $2 b y$ from $10 b y$ .

$2 a x - 4 a y - 4 b x + 8 b y$

Step 9

Rewrite $2 a x - 4 a y - 4 b x + 8 b y$ in a factored form.

Tap for more steps...

Step 9.1

Factor $2$ out of $2 a x - 4 a y - 4 b x + 8 b y$ .

Tap for more steps...

Step 9.1.1

Factor $2$ out of $2 a x$ .

$2 (a x) - 4 a y - 4 b x + 8 b y$

Step 9.1.2

Factor $2$ out of $- 4 a y$ .

$2 (a x) + 2 (- 2 a y) - 4 b x + 8 b y$

Step 9.1.3

Factor $2$ out of $- 4 b x$ .

$2 (a x) + 2 (- 2 a y) + 2 (- 2 b x) + 8 b y$

Step 9.1.4

Factor $2$ out of $8 b y$ .

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

Step 9.1.5

Factor $2$ out of $2 (a x) + 2 (- 2 a y)$ .

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

Step 9.1.6

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

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

Step 9.1.7

Factor $2$ out of $2 (a x - 2 a y - 2 b x) + 2 (4 b y)$ .

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

Step 9.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 9.2.1

Group the first two terms and the last two terms.

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

Step 9.2.2

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

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

Step 9.3

Factor.

Tap for more steps...

Step 9.3.1

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

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

Step 9.3.2

Remove unnecessary parentheses.

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