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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