Write in Standard Form -5y^2(-3y^3+8y)

$- 5 y^{2} (- 3 y^{3} + 8 y)$

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 by multiplying through.

Apply the distributive property.

$- 5 y^{2} (- 3 y^{3}) - 5 y^{2} (8 y)$

Reorder.

Rewrite using the commutative property of multiplication.

$- 5 \cdot - 3 y^{2} y^{3} - 5 y^{2} (8 y)$

Rewrite using the commutative property of multiplication.

$- 5 \cdot - 3 y^{2} y^{3} - 5 \cdot 8 y^{2} y$

Step 3

Simplify each term.

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$- 5 \cdot - 3 (y^{3} y^{2}) - 5 \cdot 8 y^{2} y$

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

$- 5 \cdot - 3 y^{3 + 2} - 5 \cdot 8 y^{2} y$

Add $3$ and $2$ .

$- 5 \cdot - 3 y^{5} - 5 \cdot 8 y^{2} y$

Multiply $- 5$ by $- 3$ .

$15 y^{5} - 5 \cdot 8 y^{2} y$

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

Move $y$ .

$15 y^{5} - 5 \cdot 8 (y \cdot y^{2})$

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

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

$15 y^{5} - 5 \cdot 8 (y^{1} y^{2})$

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

$15 y^{5} - 5 \cdot 8 y^{1 + 2}$

Add $1$ and $2$ .

$15 y^{5} - 5 \cdot 8 y^{3}$

Multiply $- 5$ by $8$ .

$15 y^{5} - 40 y^{3}$