Chemistry Examples

$(5 v + 3 x + 4) (7 v - 6)$

Step 1

Expand $(5 v + 3 x + 4) (7 v - 6)$ by multiplying each term in the first expression by each term in the second expression.

$5 v (7 v) + 5 v \cdot - 6 + 3 x (7 v) + 3 x \cdot - 6 + 4 (7 v) + 4 \cdot - 6$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 7 v \cdot v + 5 v \cdot - 6 + 3 x (7 v) + 3 x \cdot - 6 + 4 (7 v) + 4 \cdot - 6$

Step 2.1.2

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

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Step 2.1.2.1

Move $v$ .

$5 \cdot 7 (v \cdot v) + 5 v \cdot - 6 + 3 x (7 v) + 3 x \cdot - 6 + 4 (7 v) + 4 \cdot - 6$

Step 2.1.2.2

Multiply $v$ by $v$ .

$5 \cdot 7 v^{2} + 5 v \cdot - 6 + 3 x (7 v) + 3 x \cdot - 6 + 4 (7 v) + 4 \cdot - 6$

Step 2.1.3

Multiply $5$ by $7$ .

$35 v^{2} + 5 v \cdot - 6 + 3 x (7 v) + 3 x \cdot - 6 + 4 (7 v) + 4 \cdot - 6$

Step 2.1.4

Multiply $- 6$ by $5$ .

$35 v^{2} - 30 v + 3 x (7 v) + 3 x \cdot - 6 + 4 (7 v) + 4 \cdot - 6$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$35 v^{2} - 30 v + 3 \cdot 7 x v + 3 x \cdot - 6 + 4 (7 v) + 4 \cdot - 6$

Step 2.1.6

Multiply $3$ by $7$ .

$35 v^{2} - 30 v + 21 x v + 3 x \cdot - 6 + 4 (7 v) + 4 \cdot - 6$

Step 2.1.7

Multiply $- 6$ by $3$ .

$35 v^{2} - 30 v + 21 x v - 18 x + 4 (7 v) + 4 \cdot - 6$

Step 2.1.8

Multiply $7$ by $4$ .

$35 v^{2} - 30 v + 21 x v - 18 x + 28 v + 4 \cdot - 6$

Step 2.1.9

Multiply $4$ by $- 6$ .

$35 v^{2} - 30 v + 21 x v - 18 x + 28 v - 24$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 30 v$ and $28 v$ .

$35 v^{2} - 2 v + 21 x v - 18 x - 24$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Move $x$ .

$35 v^{2} - 2 v + 21 v x - 18 x - 24$

Step 2.2.2.2

Move $- 2 v$ .

$35 v^{2} + 21 v x - 18 x - 2 v - 24$

Step 2.2.2.3

Reorder $35 v^{2}$ and $21 v x$ .

$21 v x + 35 v^{2} - 18 x - 2 v - 24$