Pre-Algebra Examples

$5 v (v - 6) + v (10 - 2 v)$ , $- (n + 5) + 10 n (7 n + 7)$

Step 1

Apply the distributive property.

$5 v \cdot v + 5 v \cdot - 6 + v (10 - 2 v) - (n + 5) + 10 n (7 n + 7)$

Step 2

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

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Step 2.1

Move $v$ .

$5 (v \cdot v) + 5 v \cdot - 6 + v (10 - 2 v) - (n + 5) + 10 n (7 n + 7)$

Step 2.2

Multiply $v$ by $v$ .

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

Step 3

Multiply $- 6$ by $5$ .

$5 v^{2} - 30 v + v (10 - 2 v) - (n + 5) + 10 n (7 n + 7)$

Step 4

Apply the distributive property.

$5 v^{2} - 30 v + v \cdot 10 + v (- 2 v) - (n + 5) + 10 n (7 n + 7)$

Step 5

Move $10$ to the left of $v$ .

$5 v^{2} - 30 v + 10 \cdot v + v (- 2 v) - (n + 5) + 10 n (7 n + 7)$

Step 6

Rewrite using the commutative property of multiplication.

$5 v^{2} - 30 v + 10 v - 2 v \cdot v - (n + 5) + 10 n (7 n + 7)$

Step 7

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

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Step 7.1

Move $v$ .

$5 v^{2} - 30 v + 10 v - 2 (v \cdot v) - (n + 5) + 10 n (7 n + 7)$

Step 7.2

Multiply $v$ by $v$ .

$5 v^{2} - 30 v + 10 v - 2 v^{2} - (n + 5) + 10 n (7 n + 7)$

Step 8

Apply the distributive property.

$5 v^{2} - 30 v + 10 v - 2 v^{2} - n - 1 \cdot 5 + 10 n (7 n + 7)$

Step 9

Multiply $- 1$ by $5$ .

$5 v^{2} - 30 v + 10 v - 2 v^{2} - n - 5 + 10 n (7 n + 7)$

Step 10

Apply the distributive property.

$5 v^{2} - 30 v + 10 v - 2 v^{2} - n - 5 + 10 n (7 n) + 10 n \cdot 7$

Step 11

Rewrite using the commutative property of multiplication.

$5 v^{2} - 30 v + 10 v - 2 v^{2} - n - 5 + 10 \cdot 7 n \cdot n + 10 n \cdot 7$

Step 12

Multiply $7$ by $10$ .

$5 v^{2} - 30 v + 10 v - 2 v^{2} - n - 5 + 10 \cdot 7 n \cdot n + 70 n$

Step 13

Simplify each term.

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Step 13.1

Multiply $n$ by $n$ by adding the exponents.

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Step 13.1.1

Move $n$ .

$5 v^{2} - 30 v + 10 v - 2 v^{2} - n - 5 + 10 \cdot 7 (n \cdot n) + 70 n$

Step 13.1.2

Multiply $n$ by $n$ .

$5 v^{2} - 30 v + 10 v - 2 v^{2} - n - 5 + 10 \cdot 7 n^{2} + 70 n$

Step 13.2

Multiply $10$ by $7$ .

$5 v^{2} - 30 v + 10 v - 2 v^{2} - n - 5 + 70 n^{2} + 70 n$

Step 14

Subtract $2 v^{2}$ from $5 v^{2}$ .

$3 v^{2} - 30 v + 10 v - n - 5 + 70 n^{2} + 70 n$

Step 15

Add $- 30 v$ and $10 v$ .

$3 v^{2} - 20 v - n - 5 + 70 n^{2} + 70 n$

Step 16

Add $- n$ and $70 n$ .

$3 v^{2} - 20 v + 69 n - 5 + 70 n^{2}$

Step 17

Since there are no common prime factors, the GCF is $1$ .

$1$