Pre-Algebra Examples

$(3 v + 6 u + 7) (4 v - u)$

Step 1

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

$3 v (4 v) + 3 v (- u) + 6 u (4 v) + 6 u (- u) + 7 (4 v) + 7 (- u)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

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

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Step 2.2.1

Move $v$ .

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

Step 2.2.2

Multiply $v$ by $v$ .

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

Step 2.3

Multiply $3$ by $4$ .

$12 v^{2} + 3 v (- u) + 6 u (4 v) + 6 u (- u) + 7 (4 v) + 7 (- u)$

Step 2.4

Rewrite using the commutative property of multiplication.

$12 v^{2} + 3 \cdot - 1 v u + 6 u (4 v) + 6 u (- u) + 7 (4 v) + 7 (- u)$

Step 2.5

Multiply $3$ by $- 1$ .

$12 v^{2} - 3 v u + 6 u (4 v) + 6 u (- u) + 7 (4 v) + 7 (- u)$

Step 2.6

Rewrite using the commutative property of multiplication.

$12 v^{2} - 3 v u + 6 \cdot 4 u v + 6 u (- u) + 7 (4 v) + 7 (- u)$

Step 2.7

Multiply $6$ by $4$ .

$12 v^{2} - 3 v u + 24 u v + 6 u (- u) + 7 (4 v) + 7 (- u)$

Step 2.8

Rewrite using the commutative property of multiplication.

$12 v^{2} - 3 v u + 24 u v + 6 \cdot - 1 u \cdot u + 7 (4 v) + 7 (- u)$

Step 2.9

Multiply $u$ by $u$ by adding the exponents.

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Step 2.9.1

Move $u$ .

$12 v^{2} - 3 v u + 24 u v + 6 \cdot - 1 (u \cdot u) + 7 (4 v) + 7 (- u)$

Step 2.9.2

Multiply $u$ by $u$ .

$12 v^{2} - 3 v u + 24 u v + 6 \cdot - 1 u^{2} + 7 (4 v) + 7 (- u)$

Step 2.10

Multiply $6$ by $- 1$ .

$12 v^{2} - 3 v u + 24 u v - 6 u^{2} + 7 (4 v) + 7 (- u)$

Step 2.11

Multiply $4$ by $7$ .

$12 v^{2} - 3 v u + 24 u v - 6 u^{2} + 28 v + 7 (- u)$

Step 2.12

Multiply $- 1$ by $7$ .

$12 v^{2} - 3 v u + 24 u v - 6 u^{2} + 28 v - 7 u$

Step 3

Add $- 3 v u$ and $24 u v$ .

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Step 3.1

Move $v$ .

$12 v^{2} - 3 u v + 24 u v - 6 u^{2} + 28 v - 7 u$

Step 3.2

Add $- 3 u v$ and $24 u v$ .

$12 v^{2} + 21 u v - 6 u^{2} + 28 v - 7 u$

Step 4

Move $28 v$ .

$12 v^{2} + 21 u v - 6 u^{2} - 7 u + 28 v$

Step 5

Move $12 v^{2}$ .

$21 u v - 6 u^{2} + 12 v^{2} - 7 u + 28 v$

Step 6

Reorder $21 u v$ and $- 6 u^{2}$ .

$- 6 u^{2} + 21 u v + 12 v^{2} - 7 u + 28 v$