Trigonometry Examples

$(7 v - 5 x - 3) (6 v - 2)$

Step 1

Expand $(7 v - 5 x - 3) (6 v - 2)$ by multiplying each term in the first expression by each term in the second expression.

$7 v (6 v) + 7 v \cdot - 2 - 5 x (6 v) - 5 x \cdot - 2 - 3 (6 v) - 3 \cdot - 2$

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.

$7 \cdot 6 v \cdot v + 7 v \cdot - 2 - 5 x (6 v) - 5 x \cdot - 2 - 3 (6 v) - 3 \cdot - 2$

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

Move $v$ .

$7 \cdot 6 (v \cdot v) + 7 v \cdot - 2 - 5 x (6 v) - 5 x \cdot - 2 - 3 (6 v) - 3 \cdot - 2$

Step 2.1.2.2

Multiply $v$ by $v$ .

$7 \cdot 6 v^{2} + 7 v \cdot - 2 - 5 x (6 v) - 5 x \cdot - 2 - 3 (6 v) - 3 \cdot - 2$

Step 2.1.3

Multiply $7$ by $6$ .

$42 v^{2} + 7 v \cdot - 2 - 5 x (6 v) - 5 x \cdot - 2 - 3 (6 v) - 3 \cdot - 2$

Step 2.1.4

Multiply $- 2$ by $7$ .

$42 v^{2} - 14 v - 5 x (6 v) - 5 x \cdot - 2 - 3 (6 v) - 3 \cdot - 2$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$42 v^{2} - 14 v - 5 \cdot 6 x v - 5 x \cdot - 2 - 3 (6 v) - 3 \cdot - 2$

Step 2.1.6

Multiply $- 5$ by $6$ .

$42 v^{2} - 14 v - 30 x v - 5 x \cdot - 2 - 3 (6 v) - 3 \cdot - 2$

Step 2.1.7

Multiply $- 2$ by $- 5$ .

$42 v^{2} - 14 v - 30 x v + 10 x - 3 (6 v) - 3 \cdot - 2$

Step 2.1.8

Multiply $6$ by $- 3$ .

$42 v^{2} - 14 v - 30 x v + 10 x - 18 v - 3 \cdot - 2$

Step 2.1.9

Multiply $- 3$ by $- 2$ .

$42 v^{2} - 14 v - 30 x v + 10 x - 18 v + 6$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Subtract $18 v$ from $- 14 v$ .

$42 v^{2} - 32 v - 30 x v + 10 x + 6$

Step 2.2.2

Simplify the expression.

Tap for more steps...

Step 2.2.2.1

Move $x$ .

$42 v^{2} - 32 v - 30 v x + 10 x + 6$

Step 2.2.2.2

Move $- 32 v$ .

$42 v^{2} - 30 v x + 10 x - 32 v + 6$

Step 2.2.2.3

Reorder $42 v^{2}$ and $- 30 v x$ .

$- 30 v x + 42 v^{2} + 10 x - 32 v + 6$