Algebra Examples

$(30 x^{4} + 12 x^{3} + 30 x^{2}) \div 6$

Step 1

Rewrite the division as a fraction.

$\frac{30 x^{4} + 12 x^{3} + 30 x^{2}}{6}$

Step 2

Factor $6 x^{2}$ out of $30 x^{4} + 12 x^{3} + 30 x^{2}$ .

Tap for more steps...

Step 2.1

Factor $6 x^{2}$ out of $30 x^{4}$ .

$\frac{6 x^{2} (5 x^{2}) + 12 x^{3} + 30 x^{2}}{6}$

Step 2.2

Factor $6 x^{2}$ out of $12 x^{3}$ .

$\frac{6 x^{2} (5 x^{2}) + 6 x^{2} (2 x) + 30 x^{2}}{6}$

Step 2.3

Factor $6 x^{2}$ out of $30 x^{2}$ .

$\frac{6 x^{2} (5 x^{2}) + 6 x^{2} (2 x) + 6 x^{2} (5)}{6}$

Step 2.4

Factor $6 x^{2}$ out of $6 x^{2} (5 x^{2}) + 6 x^{2} (2 x)$ .

$\frac{6 x^{2} (5 x^{2} + 2 x) + 6 x^{2} (5)}{6}$

Step 2.5

Factor $6 x^{2}$ out of $6 x^{2} (5 x^{2} + 2 x) + 6 x^{2} (5)$ .

$\frac{6 x^{2} (5 x^{2} + 2 x + 5)}{6}$

Step 3

Cancel the common factor of $6$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{6 x^{2} (5 x^{2} + 2 x + 5)}{6}$

Step 3.2

Divide $x^{2} (5 x^{2} + 2 x + 5)$ by $1$ .

$x^{2} (5 x^{2} + 2 x + 5)$

Step 4

Apply the distributive property.

$x^{2} (5 x^{2}) + x^{2} (2 x) + x^{2} \cdot 5$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Rewrite using the commutative property of multiplication.

$5 x^{2} x^{2} + x^{2} (2 x) + x^{2} \cdot 5$

Step 5.2

Rewrite using the commutative property of multiplication.

$5 x^{2} x^{2} + 2 x^{2} x + x^{2} \cdot 5$

Step 5.3

Move $5$ to the left of $x^{2}$ .

$5 x^{2} x^{2} + 2 x^{2} x + 5 \cdot x^{2}$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

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

Tap for more steps...

Step 6.1.1

Move $x^{2}$ .

$5 (x^{2} x^{2}) + 2 x^{2} x + 5 \cdot x^{2}$

Step 6.1.2

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

$5 x^{2 + 2} + 2 x^{2} x + 5 \cdot x^{2}$

Step 6.1.3

Add $2$ and $2$ .

$5 x^{4} + 2 x^{2} x + 5 \cdot x^{2}$

Step 6.2

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

Tap for more steps...

Step 6.2.1

Move $x$ .

$5 x^{4} + 2 (x \cdot x^{2}) + 5 \cdot x^{2}$

Step 6.2.2

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

Tap for more steps...

Step 6.2.2.1

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

$5 x^{4} + 2 (x^{1} x^{2}) + 5 \cdot x^{2}$

Step 6.2.2.2

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

$5 x^{4} + 2 x^{1 + 2} + 5 \cdot x^{2}$

Step 6.2.3

Add $1$ and $2$ .

$5 x^{4} + 2 x^{3} + 5 \cdot x^{2}$

$5 x^{4} + 2 x^{3} + 5 x^{2}$