Algebra Examples

$\frac{4 j k^{2} - 2 j^{3} k^{4}}{2 j k}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Factor $2 j k^{2}$ out of $4 j k^{2} - 2 j^{3} k^{4}$ .

Tap for more steps...

Step 1.1.1

Factor $2 j k^{2}$ out of $4 j k^{2}$ .

$\frac{2 j k^{2} (2) - 2 j^{3} k^{4}}{2 j k}$

Step 1.1.2

Factor $2 j k^{2}$ out of $- 2 j^{3} k^{4}$ .

$\frac{2 j k^{2} (2) + 2 j k^{2} (- j^{2} k^{2})}{2 j k}$

Step 1.1.3

Factor $2 j k^{2}$ out of $2 j k^{2} (2) + 2 j k^{2} (- j^{2} k^{2})$ .

$\frac{2 j k^{2} (2 - j^{2} k^{2})}{2 j k}$

Step 1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$\frac{2 j k^{2} (2 - j^{2} k^{2})}{2 j k}$

Step 1.2.2

Rewrite the expression.

$\frac{j k^{2} (2 - j^{2} k^{2})}{j k}$

Step 1.3

Cancel the common factor of $j$ .

Tap for more steps...

Step 1.3.1

Cancel the common factor.

$\frac{j k^{2} (2 - j^{2} k^{2})}{j k}$

Step 1.3.2

Rewrite the expression.

$\frac{k^{2} (2 - j^{2} k^{2})}{k}$

Step 1.4

Cancel the common factor of $k^{2}$ and $k$ .

Tap for more steps...

Step 1.4.1

Factor $k$ out of $k^{2} (2 - j^{2} k^{2})$ .

$\frac{k (k (2 - j^{2} k^{2}))}{k}$

Step 1.4.2

Cancel the common factors.

Tap for more steps...

Step 1.4.2.1

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

$\frac{k (k (2 - j^{2} k^{2}))}{k^{1}}$

Step 1.4.2.2

Factor $k$ out of $k^{1}$ .

$\frac{k (k (2 - j^{2} k^{2}))}{k \cdot 1}$

Step 1.4.2.3

Cancel the common factor.

$\frac{k (k (2 - j^{2} k^{2}))}{k \cdot 1}$

Step 1.4.2.4

Rewrite the expression.

$\frac{k (2 - j^{2} k^{2})}{1}$

Step 1.4.2.5

Divide $k (2 - j^{2} k^{2})$ by $1$ .

$k (2 - j^{2} k^{2})$

Step 1.5

Apply the distributive property.

$k \cdot 2 + k (- j^{2} k^{2})$

Step 1.6

Reorder.

Tap for more steps...

Step 1.6.1

Move $2$ to the left of $k$ .

$2 \cdot k + k (- j^{2} k^{2})$

Step 1.6.2

Rewrite using the commutative property of multiplication.

$2 \cdot k - k (j^{2} k^{2})$

Step 2

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

Tap for more steps...

Step 2.1

Move $k^{2}$ .

$2 k - (k^{2} k) j^{2}$

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

$2 k - (k^{2} k^{1}) j^{2}$

Step 2.2.2

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

$2 k - k^{2 + 1} j^{2}$

Step 2.3

Add $2$ and $1$ .

$2 k - k^{3} j^{2}$