Simplify 2j(7j^2k^2+jk^2+5k)-9k(-2j^2k^2+2k^2+3j)

$2 j (7 j^{2} k^{2} + j k^{2} + 5 k) - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Step 1

Simplify each term.

Apply the distributive property.

$2 j (7 j^{2} k^{2}) + 2 j (j k^{2}) + 2 j (5 k) - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Simplify.

Multiply $j$ by $j^{2}$ by adding the exponents.

Move $j^{2}$ .

$2 (j^{2} j) (7 k^{2}) + 2 j (j k^{2}) + 2 j (5 k) - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Multiply $j^{2}$ by $j$ .

Raise $j$ to the power of $1$ .

$2 (j^{2} j^{1}) (7 k^{2}) + 2 j (j k^{2}) + 2 j (5 k) - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 j^{2 + 1} (7 k^{2}) + 2 j (j k^{2}) + 2 j (5 k) - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Add $2$ and $1$ .

$2 j^{3} (7 k^{2}) + 2 j (j k^{2}) + 2 j (5 k) - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Multiply $j$ by $j$ by adding the exponents.

Move $j$ .

$2 j^{3} (7 k^{2}) + 2 (j \cdot j) k^{2} + 2 j (5 k) - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Multiply $j$ by $j$ .

$2 j^{3} (7 k^{2}) + 2 j^{2} k^{2} + 2 j (5 k) - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Rewrite using the commutative property of multiplication.

$2 j^{3} (7 k^{2}) + 2 j^{2} k^{2} + 2 \cdot 5 j k - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 7 j^{3} k^{2} + 2 j^{2} k^{2} + 2 \cdot 5 j k - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Multiply $2$ by $7$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 2 \cdot 5 j k - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Multiply $2$ by $5$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 k (- 2 j^{2} k^{2} + 2 k^{2} + 3 j)$

Apply the distributive property.

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 k (- 2 j^{2} k^{2}) - 9 k (2 k^{2}) - 9 k (3 j)$

Simplify.

Multiply $k$ by $k^{2}$ by adding the exponents.

Move $k^{2}$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 (k^{2} k) (- 2 j^{2}) - 9 k (2 k^{2}) - 9 k (3 j)$

Multiply $k^{2}$ by $k$ .

Raise $k$ to the power of $1$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 (k^{2} k^{1}) (- 2 j^{2}) - 9 k (2 k^{2}) - 9 k (3 j)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 k^{2 + 1} (- 2 j^{2}) - 9 k (2 k^{2}) - 9 k (3 j)$

Add $2$ and $1$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 k^{3} (- 2 j^{2}) - 9 k (2 k^{2}) - 9 k (3 j)$

Rewrite using the commutative property of multiplication.

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 k^{3} (- 2 j^{2}) - 9 \cdot 2 k \cdot k^{2} - 9 k (3 j)$

Rewrite using the commutative property of multiplication.

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 k^{3} (- 2 j^{2}) - 9 \cdot 2 k \cdot k^{2} - 9 \cdot 3 k j$

Simplify each term.

Rewrite using the commutative property of multiplication.

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k - 9 \cdot - 2 k^{3} j^{2} - 9 \cdot 2 k \cdot k^{2} - 9 \cdot 3 k j$

Multiply $- 9$ by $- 2$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k + 18 k^{3} j^{2} - 9 \cdot 2 k \cdot k^{2} - 9 \cdot 3 k j$

Multiply $k$ by $k^{2}$ by adding the exponents.

Move $k^{2}$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k + 18 k^{3} j^{2} - 9 \cdot 2 (k^{2} k) - 9 \cdot 3 k j$

Multiply $k^{2}$ by $k$ .

Raise $k$ to the power of $1$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k + 18 k^{3} j^{2} - 9 \cdot 2 (k^{2} k^{1}) - 9 \cdot 3 k j$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k + 18 k^{3} j^{2} - 9 \cdot 2 k^{2 + 1} - 9 \cdot 3 k j$

Add $2$ and $1$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k + 18 k^{3} j^{2} - 9 \cdot 2 k^{3} - 9 \cdot 3 k j$

Multiply $- 9$ by $2$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k + 18 k^{3} j^{2} - 18 k^{3} - 9 \cdot 3 k j$

Multiply $- 9$ by $3$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 10 j k + 18 k^{3} j^{2} - 18 k^{3} - 27 k j$

Step 2

Subtract $27 k j$ from $10 j k$ .

Move $k$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 18 k^{3} j^{2} - 18 k^{3} + 10 j k - 27 j k$

Subtract $27 j k$ from $10 j k$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 18 k^{3} j^{2} - 18 k^{3} - 17 j k$

Step 3

Move $k^{3}$ .

$14 j^{3} k^{2} + 2 j^{2} k^{2} + 18 j^{2} k^{3} - 18 k^{3} - 17 j k$

Step 4

Move $2 j^{2} k^{2}$ .

$14 j^{3} k^{2} + 18 j^{2} k^{3} + 2 j^{2} k^{2} - 18 k^{3} - 17 j k$

Simplify 2j(7j^2k^2+jk^2+5k)-9k(-2j^2k^2+2k^2+3j)

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