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

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

Simplify each term.

Use the Binomial Theorem.

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

Simplify each term.

Multiply $4$ by $3$ .

$y^{3} + 12 y^{2} + 3 y \cdot 4^{2} + 4^{3} - 2 y (y - 1)$

Raise $4$ to the power of $2$ .

$y^{3} + 12 y^{2} + 3 y \cdot 16 + 4^{3} - 2 y (y - 1)$

Multiply $16$ by $3$ .

$y^{3} + 12 y^{2} + 48 y + 4^{3} - 2 y (y - 1)$

Raise $4$ to the power of $3$ .

$y^{3} + 12 y^{2} + 48 y + 64 - 2 y (y - 1)$

Apply the distributive property.

$y^{3} + 12 y^{2} + 48 y + 64 - 2 y \cdot y - 2 y \cdot - 1$

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

Move $y$ .

$y^{3} + 12 y^{2} + 48 y + 64 - 2 (y \cdot y) - 2 y \cdot - 1$

Multiply $y$ by $y$ .

$y^{3} + 12 y^{2} + 48 y + 64 - 2 y^{2} - 2 y \cdot - 1$

Multiply $- 1$ by $- 2$ .

$y^{3} + 12 y^{2} + 48 y + 64 - 2 y^{2} + 2 y$

Simplify by adding terms.

Subtract $2 y^{2}$ from $12 y^{2}$ .

$y^{3} + 10 y^{2} + 48 y + 64 + 2 y$

Add $48 y$ and $2 y$ .

$y^{3} + 10 y^{2} + 50 y + 64$