Simplify 4s^2y(2s^3y+3s^2y^2+8y^3)

$4 s^{2} y (2 s^{3} y + 3 s^{2} y^{2} + 8 y^{3})$

Step 1

Apply the distributive property.

$4 s^{2} y (2 s^{3} y) + 4 s^{2} y (3 s^{2} y^{2}) + 4 s^{2} y (8 y^{3})$

Step 2

Simplify.

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

Move $s^{3}$ .

$4 (s^{3} s^{2}) y (2 y) + 4 s^{2} y (3 s^{2} y^{2}) + 4 s^{2} y (8 y^{3})$

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

$4 s^{3 + 2} y (2 y) + 4 s^{2} y (3 s^{2} y^{2}) + 4 s^{2} y (8 y^{3})$

Add $3$ and $2$ .

$4 s^{5} y (2 y) + 4 s^{2} y (3 s^{2} y^{2}) + 4 s^{2} y (8 y^{3})$

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

Move $s^{2}$ .

$4 s^{5} y (2 y) + 4 (s^{2} s^{2}) y (3 y^{2}) + 4 s^{2} y (8 y^{3})$

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

$4 s^{5} y (2 y) + 4 s^{2 + 2} y (3 y^{2}) + 4 s^{2} y (8 y^{3})$

Add $2$ and $2$ .

$4 s^{5} y (2 y) + 4 s^{4} y (3 y^{2}) + 4 s^{2} y (8 y^{3})$

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

Move $y^{3}$ .

$4 s^{5} y (2 y) + 4 s^{4} y (3 y^{2}) + 4 s^{2} (y^{3} y) \cdot 8$

Multiply $y^{3}$ by $y$ .

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

$4 s^{5} y (2 y) + 4 s^{4} y (3 y^{2}) + 4 s^{2} (y^{3} y^{1}) \cdot 8$

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

$4 s^{5} y (2 y) + 4 s^{4} y (3 y^{2}) + 4 s^{2} y^{3 + 1} \cdot 8$

Add $3$ and $1$ .

$4 s^{5} y (2 y) + 4 s^{4} y (3 y^{2}) + 4 s^{2} y^{4} \cdot 8$

Step 3

Simplify each term.

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

Move $y$ .

$4 s^{5} (y \cdot y) \cdot 2 + 4 s^{4} y (3 y^{2}) + 4 s^{2} y^{4} \cdot 8$

Multiply $y$ by $y$ .

$4 s^{5} y^{2} \cdot 2 + 4 s^{4} y (3 y^{2}) + 4 s^{2} y^{4} \cdot 8$

Multiply $2$ by $4$ .

$8 s^{5} y^{2} + 4 s^{4} y (3 y^{2}) + 4 s^{2} y^{4} \cdot 8$

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

Move $y^{2}$ .

$8 s^{5} y^{2} + 4 s^{4} (y^{2} y) \cdot 3 + 4 s^{2} y^{4} \cdot 8$

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

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

$8 s^{5} y^{2} + 4 s^{4} (y^{2} y^{1}) \cdot 3 + 4 s^{2} y^{4} \cdot 8$

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

$8 s^{5} y^{2} + 4 s^{4} y^{2 + 1} \cdot 3 + 4 s^{2} y^{4} \cdot 8$

Add $2$ and $1$ .

$8 s^{5} y^{2} + 4 s^{4} y^{3} \cdot 3 + 4 s^{2} y^{4} \cdot 8$

Multiply $3$ by $4$ .

$8 s^{5} y^{2} + 12 s^{4} y^{3} + 4 s^{2} y^{4} \cdot 8$

Multiply $8$ by $4$ .

$8 s^{5} y^{2} + 12 s^{4} y^{3} + 32 s^{2} y^{4}$

Simplify 4s^2y(2s^3y+3s^2y^2+8y^3)

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