Find the Product 5r^5(6r-3)

$5 r^{5} (6 r - 3)$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$5 r^{5} (6 r) + 5 r^{5} \cdot - 3$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$5 \cdot 6 r^{5} r + 5 r^{5} \cdot - 3$

Multiply $- 3$ by $5$ .

$5 \cdot 6 r^{5} r - 15 r^{5}$

Step 2

Simplify each term.

Multiply $r^{5}$ by $r$ by adding the exponents.

Move $r$ .

$5 \cdot 6 (r \cdot r^{5}) - 15 r^{5}$

Multiply $r$ by $r^{5}$ .

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

$5 \cdot 6 (r^{1} r^{5}) - 15 r^{5}$

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

$5 \cdot 6 r^{1 + 5} - 15 r^{5}$

Add $1$ and $5$ .

$5 \cdot 6 r^{6} - 15 r^{5}$

Multiply $5$ by $6$ .

$30 r^{6} - 15 r^{5}$