Algebra Examples

$(2 x - 3 y) (x + 2 y)$

Step 1

Expand $(2 x - 3 y) (x + 2 y)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$2 x (x + 2 y) - 3 y (x + 2 y)$

Step 1.2

Apply the distributive property.

$2 x \cdot x + 2 x (2 y) - 3 y (x + 2 y)$

Step 1.3

Apply the distributive property.

$2 x \cdot x + 2 x (2 y) - 3 y x - 3 y (2 y)$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

Tap for more steps...

Step 2.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x (2 y) - 3 y x - 3 y (2 y)$

Step 2.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x (2 y) - 3 y x - 3 y (2 y)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$2 x^{2} + 2 \cdot 2 x y - 3 y x - 3 y (2 y)$

Step 2.1.3

Multiply $2$ by $2$ .

$2 x^{2} + 4 x y - 3 y x - 3 y (2 y)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$2 x^{2} + 4 x y - 3 y x - 3 \cdot 2 y \cdot y$

Step 2.1.5

Multiply $y$ by $y$ by adding the exponents.

Tap for more steps...

Step 2.1.5.1

Move $y$ .

$2 x^{2} + 4 x y - 3 y x - 3 \cdot 2 (y \cdot y)$

Step 2.1.5.2

Multiply $y$ by $y$ .

$2 x^{2} + 4 x y - 3 y x - 3 \cdot 2 y^{2}$

Step 2.1.6

Multiply $- 3$ by $2$ .

$2 x^{2} + 4 x y - 3 y x - 6 y^{2}$

Step 2.2

Subtract $3 y x$ from $4 x y$ .

Tap for more steps...

Step 2.2.1

Move $y$ .

$2 x^{2} + 4 x y - 3 x y - 6 y^{2}$

Step 2.2.2

Subtract $3 x y$ from $4 x y$ .

$2 x^{2} + 1 x y - 6 y^{2}$

Step 3

Multiply $x$ by $1$ .

$2 x^{2} + x y - 6 y^{2}$