Basic Math Examples

$(- 7 x - 4 y) (2 x + 3 y)$

Step 1

Expand

$(- 7 x - 4 y) (2 x + 3 y)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$- 7 x (2 x + 3 y) - 4 y (2 x + 3 y)$

Step 1.2

Apply the distributive property.

$- 7 x (2 x) - 7 x (3 y) - 4 y (2 x + 3 y)$

Step 1.3

Apply the distributive property.

$- 7 x (2 x) - 7 x (3 y) - 4 y (2 x) - 4 y (3 y)$

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

Rewrite using the commutative property of multiplication.

$- 7 \cdot 2 x \cdot x - 7 x (3 y) - 4 y (2 x) - 4 y (3 y)$

Step 2.1.2

Multiply

$x$ by

$x$ by adding the exponents.

Tap for more steps...

Step 2.1.2.1

Move

$x$ .

$- 7 \cdot 2 (x \cdot x) - 7 x (3 y) - 4 y (2 x) - 4 y (3 y)$

Step 2.1.2.2

Multiply

$x$ by

$x$ .

$- 7 \cdot 2 x^{2} - 7 x (3 y) - 4 y (2 x) - 4 y (3 y)$

Step 2.1.3

Multiply

$- 7$ by

$2$ .

$- 14 x^{2} - 7 x (3 y) - 4 y (2 x) - 4 y (3 y)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$- 14 x^{2} - 7 \cdot 3 x y - 4 y (2 x) - 4 y (3 y)$

Step 2.1.5

Multiply

$- 7$ by

$3$ .

$- 14 x^{2} - 21 x y - 4 y (2 x) - 4 y (3 y)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$- 14 x^{2} - 21 x y - 4 \cdot 2 y x - 4 y (3 y)$

Step 2.1.7

Multiply

$- 4$ by

$2$ .

$- 14 x^{2} - 21 x y - 8 y x - 4 y (3 y)$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$- 14 x^{2} - 21 x y - 8 y x - 4 \cdot 3 y \cdot y$

Step 2.1.9

Multiply

$y$ by

$y$ by adding the exponents.

Tap for more steps...

Step 2.1.9.1

Move

$y$ .

$- 14 x^{2} - 21 x y - 8 y x - 4 \cdot 3 (y \cdot y)$

Step 2.1.9.2

Multiply

$y$ by

$y$ .

$- 14 x^{2} - 21 x y - 8 y x - 4 \cdot 3 y^{2}$

Step 2.1.10

Multiply

$- 4$ by

$3$ .

$- 14 x^{2} - 21 x y - 8 y x - 12 y^{2}$

Step 2.2

Subtract

$8 y x$ from

$- 21 x y$ .

Tap for more steps...

Step 2.2.1

Move

$y$ .

$- 14 x^{2} - 21 x y - 8 x y - 12 y^{2}$

Step 2.2.2

Subtract

$8 x y$ from

$- 21 x y$ .

$- 14 x^{2} - 29 x y - 12 y^{2}$