Simplify 3y^3-2y(4y-y(y-3))-(2y(y+1)-3y(y^2-1))

$3 y^{3} - 2 y (4 y - y (y - 3)) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Step 1

Simplify each term.

Apply the distributive property.

$3 y^{3} - 2 y (4 y - y \cdot y - y \cdot - 3) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$3 y^{3} - 2 y (4 y - (y \cdot y) - y \cdot - 3) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Multiply $y$ by $y$ .

$3 y^{3} - 2 y (4 y - y^{2} - y \cdot - 3) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Multiply $- 3$ by $- 1$ .

$3 y^{3} - 2 y (4 y - y^{2} + 3 y) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Add $4 y$ and $3 y$ .

$3 y^{3} - 2 y (- y^{2} + 7 y) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Apply the distributive property.

$3 y^{3} - 2 y (- y^{2}) - 2 y (7 y) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Rewrite using the commutative property of multiplication.

$3 y^{3} - 2 \cdot - 1 y \cdot y^{2} - 2 y (7 y) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Rewrite using the commutative property of multiplication.

$3 y^{3} - 2 \cdot - 1 y \cdot y^{2} - 2 \cdot 7 y \cdot y - (2 y (y + 1) - 3 y (y^{2} - 1))$

Simplify each term.

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

Move $y^{2}$ .

$3 y^{3} - 2 \cdot - 1 (y^{2} y) - 2 \cdot 7 y \cdot y - (2 y (y + 1) - 3 y (y^{2} - 1))$

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

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

$3 y^{3} - 2 \cdot - 1 (y^{2} y^{1}) - 2 \cdot 7 y \cdot y - (2 y (y + 1) - 3 y (y^{2} - 1))$

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

$3 y^{3} - 2 \cdot - 1 y^{2 + 1} - 2 \cdot 7 y \cdot y - (2 y (y + 1) - 3 y (y^{2} - 1))$

Add $2$ and $1$ .

$3 y^{3} - 2 \cdot - 1 y^{3} - 2 \cdot 7 y \cdot y - (2 y (y + 1) - 3 y (y^{2} - 1))$

Multiply $- 2$ by $- 1$ .

$3 y^{3} + 2 y^{3} - 2 \cdot 7 y \cdot y - (2 y (y + 1) - 3 y (y^{2} - 1))$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$3 y^{3} + 2 y^{3} - 2 \cdot 7 (y \cdot y) - (2 y (y + 1) - 3 y (y^{2} - 1))$

Multiply $y$ by $y$ .

$3 y^{3} + 2 y^{3} - 2 \cdot 7 y^{2} - (2 y (y + 1) - 3 y (y^{2} - 1))$

Multiply $- 2$ by $7$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y (y + 1) - 3 y (y^{2} - 1))$

Simplify each term.

Apply the distributive property.

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y \cdot y + 2 y \cdot 1 - 3 y (y^{2} - 1))$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 (y \cdot y) + 2 y \cdot 1 - 3 y (y^{2} - 1))$

Multiply $y$ by $y$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} + 2 y \cdot 1 - 3 y (y^{2} - 1))$

Multiply $2$ by $1$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} + 2 y - 3 y (y^{2} - 1))$

Apply the distributive property.

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} + 2 y - 3 y \cdot y^{2} - 3 y \cdot - 1)$

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

Move $y^{2}$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} + 2 y - 3 (y^{2} y) - 3 y \cdot - 1)$

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

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

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} + 2 y - 3 (y^{2} y^{1}) - 3 y \cdot - 1)$

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

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} + 2 y - 3 y^{2 + 1} - 3 y \cdot - 1)$

Add $2$ and $1$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} + 2 y - 3 y^{3} - 3 y \cdot - 1)$

Multiply $- 1$ by $- 3$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} + 2 y - 3 y^{3} + 3 y)$

Add $2 y$ and $3 y$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2} - 3 y^{3} + 5 y)$

Apply the distributive property.

$3 y^{3} + 2 y^{3} - 14 y^{2} - (2 y^{2}) - (- 3 y^{3}) - (5 y)$

Simplify.

Multiply $2$ by $- 1$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - 2 y^{2} - (- 3 y^{3}) - (5 y)$

Multiply $- 3$ by $- 1$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - 2 y^{2} + 3 y^{3} - (5 y)$

Multiply $5$ by $- 1$ .

$3 y^{3} + 2 y^{3} - 14 y^{2} - 2 y^{2} + 3 y^{3} - 5 y$

Step 2

Simplify by adding terms.

Add $3 y^{3}$ and $2 y^{3}$ .

$5 y^{3} - 14 y^{2} - 2 y^{2} + 3 y^{3} - 5 y$

Add $5 y^{3}$ and $3 y^{3}$ .

$8 y^{3} - 14 y^{2} - 2 y^{2} - 5 y$

Subtract $2 y^{2}$ from $- 14 y^{2}$ .

$8 y^{3} - 16 y^{2} - 5 y$

Simplify 3y^3-2y(4y-y(y-3))-(2y(y+1)-3y(y^2-1))

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