Simplify 3ab(2ac+3bc)

$3 a b (2 a c + 3 b c)$

Step 1

Apply the distributive property.

$3 a b (2 a c) + 3 a b (3 b c)$

Step 2

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

Move $a$ .

$3 (a \cdot a) b (2 c) + 3 a b (3 b c)$

Multiply $a$ by $a$ .

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

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

Step 3

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

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

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

Step 4

Simplify each term.

Multiply $2$ by $3$ .

$6 a^{2} b c + 3 a b^{2} (3 c)$

Multiply $3$ by $3$ .

$6 a^{2} b c + 9 a b^{2} c$

$6 a^{2} b c + 9 a b^{2} c$

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