Simplify -5r^3(4r^2-2r-5)

$- 5 r^{3} (4 r^{2} - 2 r - 5)$

Step 1

Apply the distributive property.

$- 5 r^{3} (4 r^{2}) - 5 r^{3} (- 2 r) - 5 r^{3} \cdot - 5$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 5 \cdot 4 r^{3} r^{2} - 5 r^{3} (- 2 r) - 5 r^{3} \cdot - 5$

Rewrite using the commutative property of multiplication.

$- 5 \cdot 4 r^{3} r^{2} - 5 \cdot - 2 r^{3} r - 5 r^{3} \cdot - 5$

Multiply $- 5$ by $- 5$ .

$- 5 \cdot 4 r^{3} r^{2} - 5 \cdot - 2 r^{3} r + 25 r^{3}$

Step 3

Simplify each term.

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

Move $r^{2}$ .

$- 5 \cdot 4 (r^{2} r^{3}) - 5 \cdot - 2 r^{3} r + 25 r^{3}$

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

$- 5 \cdot 4 r^{2 + 3} - 5 \cdot - 2 r^{3} r + 25 r^{3}$

Add $2$ and $3$ .

$- 5 \cdot 4 r^{5} - 5 \cdot - 2 r^{3} r + 25 r^{3}$

Multiply $- 5$ by $4$ .

$- 20 r^{5} - 5 \cdot - 2 r^{3} r + 25 r^{3}$

Multiply $r^{3}$ by $r$ by adding the exponents.

Move $r$ .

$- 20 r^{5} - 5 \cdot - 2 (r \cdot r^{3}) + 25 r^{3}$

Multiply $r$ by $r^{3}$ .

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

$- 20 r^{5} - 5 \cdot - 2 (r^{1} r^{3}) + 25 r^{3}$

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

$- 20 r^{5} - 5 \cdot - 2 r^{1 + 3} + 25 r^{3}$

Add $1$ and $3$ .

$- 20 r^{5} - 5 \cdot - 2 r^{4} + 25 r^{3}$

Multiply $- 5$ by $- 2$ .

$- 20 r^{5} + 10 r^{4} + 25 r^{3}$