Simplify 2ab^3c(a-3b^3)

$2 a b^{3} c (a - 3 b^{3})$

Step 1

Apply the distributive property.

$2 a b^{3} c a + 2 a b^{3} c (- 3 b^{3})$

Step 2

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 (a \cdot a) b^{3} c + 2 a b^{3} c (- 3 b^{3})$

Multiply $a$ by $a$ .

$2 a^{2} b^{3} c + 2 a b^{3} c (- 3 b^{3})$

Step 3

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

Move $b^{3}$ .

$2 a^{2} b^{3} c + 2 a (b^{3} b^{3}) c \cdot - 3$

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

$2 a^{2} b^{3} c + 2 a b^{3 + 3} c \cdot - 3$

Add $3$ and $3$ .

$2 a^{2} b^{3} c + 2 a b^{6} c \cdot - 3$

Step 4

Multiply $- 3$ by $2$ .

$2 a^{2} b^{3} c - 6 a b^{6} c$