Basic Math Examples

$(2 v + y) (2 v - y - 4)$

Step 1

Expand $(2 v + y) (2 v - y - 4)$ by multiplying each term in the first expression by each term in the second expression.

$2 v (2 v) + 2 v (- y) + 2 v \cdot - 4 + y (2 v) + y (- y) + y \cdot - 4$

Step 2

Simplify 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.

$2 \cdot 2 v \cdot v + 2 v (- y) + 2 v \cdot - 4 + y (2 v) + y (- y) + y \cdot - 4$

Step 2.1.2

Multiply $v$ by $v$ by adding the exponents.

Tap for more steps...

Step 2.1.2.1

Move $v$ .

$2 \cdot 2 (v \cdot v) + 2 v (- y) + 2 v \cdot - 4 + y (2 v) + y (- y) + y \cdot - 4$

Step 2.1.2.2

Multiply $v$ by $v$ .

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

Step 2.1.3

Multiply $2$ by $2$ .

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

$4 v^{2} + 2 \cdot - 1 v y + 2 v \cdot - 4 + y (2 v) + y (- y) + y \cdot - 4$

Step 2.1.5

Multiply $2$ by $- 1$ .

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

Step 2.1.6

Multiply $- 4$ by $2$ .

$4 v^{2} - 2 v y - 8 v + y (2 v) + y (- y) + y \cdot - 4$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$4 v^{2} - 2 v y - 8 v + 2 y v + y (- y) + y \cdot - 4$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$4 v^{2} - 2 v y - 8 v + 2 y v - y \cdot y + y \cdot - 4$

Step 2.1.9

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

Tap for more steps...

Step 2.1.9.1

Move $y$ .

$4 v^{2} - 2 v y - 8 v + 2 y v - (y \cdot y) + y \cdot - 4$

Step 2.1.9.2

Multiply $y$ by $y$ .

$4 v^{2} - 2 v y - 8 v + 2 y v - y^{2} + y \cdot - 4$

Step 2.1.10

Move $- 4$ to the left of $y$ .

$4 v^{2} - 2 v y - 8 v + 2 y v - y^{2} - 4 y$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Combine the opposite terms in $4 v^{2} - 2 v y - 8 v + 2 y v - y^{2} - 4 y$ .

Tap for more steps...

Step 2.2.1.1

Reorder the factors in the terms $- 2 v y$ and $2 y v$ .

$4 v^{2} - 2 v y - 8 v + 2 v y - y^{2} - 4 y$

Step 2.2.1.2

Add $- 2 v y$ and $2 v y$ .

$4 v^{2} - 8 v + 0 - y^{2} - 4 y$

Step 2.2.1.3

Add $4 v^{2} - 8 v$ and $0$ .

$4 v^{2} - 8 v - y^{2} - 4 y$

Step 2.2.2

Move $- 8 v$ .

$4 v^{2} - y^{2} - 8 v - 4 y$