Simplify 6x^3(3x^2-x+10)

$6 x^{3} (3 x^{2} - x + 10)$

Step 1

Apply the distributive property.

$6 x^{3} (3 x^{2}) + 6 x^{3} (- x) + 6 x^{3} \cdot 10$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$6 \cdot 3 x^{3} x^{2} + 6 x^{3} (- x) + 6 x^{3} \cdot 10$

Rewrite using the commutative property of multiplication.

$6 \cdot 3 x^{3} x^{2} + 6 \cdot - 1 x^{3} x + 6 x^{3} \cdot 10$

Multiply $10$ by $6$ .

$6 \cdot 3 x^{3} x^{2} + 6 \cdot - 1 x^{3} x + 60 x^{3}$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$6 \cdot 3 (x^{2} x^{3}) + 6 \cdot - 1 x^{3} x + 60 x^{3}$

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

$6 \cdot 3 x^{2 + 3} + 6 \cdot - 1 x^{3} x + 60 x^{3}$

Add $2$ and $3$ .

$6 \cdot 3 x^{5} + 6 \cdot - 1 x^{3} x + 60 x^{3}$

Multiply $6$ by $3$ .

$18 x^{5} + 6 \cdot - 1 x^{3} x + 60 x^{3}$

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

Move $x$ .

$18 x^{5} + 6 \cdot - 1 (x \cdot x^{3}) + 60 x^{3}$

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

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

$18 x^{5} + 6 \cdot - 1 (x^{1} x^{3}) + 60 x^{3}$

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

$18 x^{5} + 6 \cdot - 1 x^{1 + 3} + 60 x^{3}$

Add $1$ and $3$ .

$18 x^{5} + 6 \cdot - 1 x^{4} + 60 x^{3}$

Multiply $6$ by $- 1$ .

$18 x^{5} - 6 x^{4} + 60 x^{3}$