Algebra Examples

$4 x (10 x^{2} + x)$

Step 1

Apply the distributive property.

$4 x (10 x^{2}) + 4 x \cdot x$

Step 2

Rewrite using the commutative property of multiplication.

$4 \cdot 10 x \cdot x^{2} + 4 x \cdot x$

Step 3

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $x$ .

$4 \cdot 10 x \cdot x^{2} + 4 (x \cdot x)$

Step 3.2

Multiply $x$ by $x$ .

$4 \cdot 10 x \cdot x^{2} + 4 x^{2}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Move $x^{2}$ .

$4 \cdot 10 (x^{2} x) + 4 x^{2}$

Step 4.1.2

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

Tap for more steps...

Step 4.1.2.1

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

$4 \cdot 10 (x^{2} x^{1}) + 4 x^{2}$

Step 4.1.2.2

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

$4 \cdot 10 x^{2 + 1} + 4 x^{2}$

Step 4.1.3

Add $2$ and $1$ .

$4 \cdot 10 x^{3} + 4 x^{2}$

Step 4.2

Multiply $4$ by $10$ .

$40 x^{3} + 4 x^{2}$