Write in Standard Form 3a(6a^2-4ab^2)+8a^2b^2-2b^3

$3 a (6 a^{2} - 4 a b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

Apply the distributive property.

$3 a (6 a^{2}) + 3 a (- 4 a b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

Rewrite using the commutative property of multiplication.

$3 \cdot 6 a \cdot a^{2} + 3 a (- 4 a b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

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

Move $a$ .

$3 \cdot 6 a \cdot a^{2} + 3 (a \cdot a) (- 4 b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

Multiply $a$ by $a$ .

$3 \cdot 6 a \cdot a^{2} + 3 a^{2} (- 4 b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

Simplify each term.

Multiply $a$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$3 \cdot 6 (a^{2} a) + 3 a^{2} (- 4 b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

Multiply $a^{2}$ by $a$ .

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

$3 \cdot 6 (a^{2} a^{1}) + 3 a^{2} (- 4 b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

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

$3 \cdot 6 a^{2 + 1} + 3 a^{2} (- 4 b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

Add $2$ and $1$ .

$3 \cdot 6 a^{3} + 3 a^{2} (- 4 b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

Multiply $3$ by $6$ .

$18 a^{3} + 3 a^{2} (- 4 b^{2}) + 8 a^{2} b^{2} - 2 b^{3}$

Rewrite using the commutative property of multiplication.

$18 a^{3} + 3 \cdot - 4 a^{2} b^{2} + 8 a^{2} b^{2} - 2 b^{3}$

Multiply $3$ by $- 4$ .

$18 a^{3} - 12 a^{2} b^{2} + 8 a^{2} b^{2} - 2 b^{3}$

Step 3

Simplify by adding terms.

Add $- 12 a^{2} b^{2}$ and $8 a^{2} b^{2}$ .

$18 a^{3} - 4 a^{2} b^{2} - 2 b^{3}$

Reorder $18 a^{3}$ and $- 4 a^{2} b^{2}$ .

$- 4 a^{2} b^{2} + 18 a^{3} - 2 b^{3}$