Pre-Algebra Examples

$\frac{1}{5} \cdot (x^{2} (20 x^{2} - 10 x + 3))$

Step 1

Apply the distributive property.

$\frac{1}{5} \cdot (x^{2} (20 x^{2}) + x^{2} (- 10 x) + x^{2} \cdot 3)$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Rewrite using the commutative property of multiplication.

$\frac{1}{5} \cdot (20 x^{2} x^{2} + x^{2} (- 10 x) + x^{2} \cdot 3)$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{1}{5} \cdot (20 x^{2} x^{2} - 10 x^{2} x + x^{2} \cdot 3)$

Step 2.3

Move $3$ to the left of $x^{2}$ .

$\frac{1}{5} \cdot (20 x^{2} x^{2} - 10 x^{2} x + 3 \cdot x^{2})$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Move $x^{2}$ .

$\frac{1}{5} \cdot (20 (x^{2} x^{2}) - 10 x^{2} x + 3 \cdot x^{2})$

Step 3.1.2

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

$\frac{1}{5} \cdot (20 x^{2 + 2} - 10 x^{2} x + 3 \cdot x^{2})$

Step 3.1.3

Add $2$ and $2$ .

$\frac{1}{5} \cdot (20 x^{4} - 10 x^{2} x + 3 \cdot x^{2})$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Move $x$ .

$\frac{1}{5} \cdot (20 x^{4} - 10 (x \cdot x^{2}) + 3 \cdot x^{2})$

Step 3.2.2

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

Tap for more steps...

Step 3.2.2.1

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

$\frac{1}{5} \cdot (20 x^{4} - 10 (x^{1} x^{2}) + 3 \cdot x^{2})$

Step 3.2.2.2

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

$\frac{1}{5} \cdot (20 x^{4} - 10 x^{1 + 2} + 3 \cdot x^{2})$

Step 3.2.3

Add $1$ and $2$ .

$\frac{1}{5} \cdot (20 x^{4} - 10 x^{3} + 3 \cdot x^{2})$

$\frac{1}{5} \cdot (20 x^{4} - 10 x^{3} + 3 x^{2})$

Step 4

Apply the distributive property.

$\frac{1}{5} (20 x^{4}) + \frac{1}{5} (- 10 x^{3}) + \frac{1}{5} (3 x^{2})$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.1.1

Factor $5$ out of $20 x^{4}$ .

$\frac{1}{5} (5 (4 x^{4})) + \frac{1}{5} (- 10 x^{3}) + \frac{1}{5} (3 x^{2})$

Step 5.1.2

Cancel the common factor.

$\frac{1}{5} (5 (4 x^{4})) + \frac{1}{5} (- 10 x^{3}) + \frac{1}{5} (3 x^{2})$

Step 5.1.3

Rewrite the expression.

$4 x^{4} + \frac{1}{5} (- 10 x^{3}) + \frac{1}{5} (3 x^{2})$

Step 5.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.2.1

Factor $5$ out of $- 10 x^{3}$ .

$4 x^{4} + \frac{1}{5} (5 (- 2 x^{3})) + \frac{1}{5} (3 x^{2})$

Step 5.2.2

Cancel the common factor.

$4 x^{4} + \frac{1}{5} (5 (- 2 x^{3})) + \frac{1}{5} (3 x^{2})$

Step 5.2.3

Rewrite the expression.

$4 x^{4} - 2 x^{3} + \frac{1}{5} (3 x^{2})$

Step 5.3

Multiply $\frac{1}{5} (3 x^{2})$ .

Tap for more steps...

Step 5.3.1

Combine $3$ and $\frac{1}{5}$ .

$4 x^{4} - 2 x^{3} + \frac{3}{5} x^{2}$

Step 5.3.2

Combine $\frac{3}{5}$ and $x^{2}$ .

$4 x^{4} - 2 x^{3} + \frac{3 x^{2}}{5}$