Basic Math Examples

$(2 u - 7 v) (5 u + 6 v - 4)$

Step 1

Expand $(2 u - 7 v) (5 u + 6 v - 4)$ by multiplying each term in the first expression by each term in the second expression.

$2 u (5 u) + 2 u (6 v) + 2 u \cdot - 4 - 7 v (5 u) - 7 v (6 v) - 7 v \cdot - 4$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 5 u \cdot u + 2 u (6 v) + 2 u \cdot - 4 - 7 v (5 u) - 7 v (6 v) - 7 v \cdot - 4$

Step 2.2

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

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Step 2.2.1

Move $u$ .

$2 \cdot 5 (u \cdot u) + 2 u (6 v) + 2 u \cdot - 4 - 7 v (5 u) - 7 v (6 v) - 7 v \cdot - 4$

Step 2.2.2

Multiply $u$ by $u$ .

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

Step 2.3

Multiply $2$ by $5$ .

$10 u^{2} + 2 u (6 v) + 2 u \cdot - 4 - 7 v (5 u) - 7 v (6 v) - 7 v \cdot - 4$

Step 2.4

Rewrite using the commutative property of multiplication.

$10 u^{2} + 2 \cdot 6 u v + 2 u \cdot - 4 - 7 v (5 u) - 7 v (6 v) - 7 v \cdot - 4$

Step 2.5

Multiply $2$ by $6$ .

$10 u^{2} + 12 u v + 2 u \cdot - 4 - 7 v (5 u) - 7 v (6 v) - 7 v \cdot - 4$

Step 2.6

Multiply $- 4$ by $2$ .

$10 u^{2} + 12 u v - 8 u - 7 v (5 u) - 7 v (6 v) - 7 v \cdot - 4$

Step 2.7

Rewrite using the commutative property of multiplication.

$10 u^{2} + 12 u v - 8 u - 7 \cdot 5 v u - 7 v (6 v) - 7 v \cdot - 4$

Step 2.8

Multiply $- 7$ by $5$ .

$10 u^{2} + 12 u v - 8 u - 35 v u - 7 v (6 v) - 7 v \cdot - 4$

Step 2.9

Rewrite using the commutative property of multiplication.

$10 u^{2} + 12 u v - 8 u - 35 v u - 7 \cdot 6 v \cdot v - 7 v \cdot - 4$

Step 2.10

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

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Step 2.10.1

Move $v$ .

$10 u^{2} + 12 u v - 8 u - 35 v u - 7 \cdot 6 (v \cdot v) - 7 v \cdot - 4$

Step 2.10.2

Multiply $v$ by $v$ .

$10 u^{2} + 12 u v - 8 u - 35 v u - 7 \cdot 6 v^{2} - 7 v \cdot - 4$

Step 2.11

Multiply $- 7$ by $6$ .

$10 u^{2} + 12 u v - 8 u - 35 v u - 42 v^{2} - 7 v \cdot - 4$

Step 2.12

Multiply $- 4$ by $- 7$ .

$10 u^{2} + 12 u v - 8 u - 35 v u - 42 v^{2} + 28 v$

Step 3

Subtract $35 v u$ from $12 u v$ .

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Step 3.1

Move $v$ .

$10 u^{2} + 12 u v - 35 u v - 8 u - 42 v^{2} + 28 v$

Step 3.2

Subtract $35 u v$ from $12 u v$ .

$10 u^{2} - 23 u v - 8 u - 42 v^{2} + 28 v$

Step 4

Move $- 8 u$ .

$10 u^{2} - 23 u v - 42 v^{2} - 8 u + 28 v$