Algebra Examples

$- 5 x^{3} y (3 x^{2} y^{2} + 15 z)$

Step 1

Apply the distributive property.

$- 5 x^{3} y (3 x^{2} y^{2}) - 5 x^{3} y (15 z)$

Step 2

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $x^{2}$ .

$- 5 (x^{2} x^{3}) y (3 y^{2}) - 5 x^{3} y (15 z)$

Step 2.2

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

$- 5 x^{2 + 3} y (3 y^{2}) - 5 x^{3} y (15 z)$

Step 2.3

Add $2$ and $3$ .

$- 5 x^{5} y (3 y^{2}) - 5 x^{3} y (15 z)$

Step 3

Multiply $15$ by $- 5$ .

$- 5 x^{5} y (3 y^{2}) - 75 x^{3} y z$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Move $y^{2}$ .

$- 5 x^{5} (y^{2} y) \cdot 3 - 75 x^{3} y z$

Step 4.1.2

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

Tap for more steps...

Step 4.1.2.1

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

$- 5 x^{5} (y^{2} y^{1}) \cdot 3 - 75 x^{3} y z$

Step 4.1.2.2

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

$- 5 x^{5} y^{2 + 1} \cdot 3 - 75 x^{3} y z$

Step 4.1.3

Add $2$ and $1$ .

$- 5 x^{5} y^{3} \cdot 3 - 75 x^{3} y z$

Step 4.2

Multiply $3$ by $- 5$ .

$- 15 x^{5} y^{3} - 75 x^{3} y z$