Simplify 3x^2y(-2x^3y^4+3x^2y+2x-8y)

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

Apply the distributive property.

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

Simplify.

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

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Simplify each term.

Multiply $y$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

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

Multiply $y^{4}$ by $y$ .

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

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

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

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

Add $4$ and $1$ .

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

Multiply $- 2$ by $3$ .

$- 6 x^{5} y^{5} + 3 x^{4} y (3 y) + 3 x^{3} y \cdot 2 + 3 x^{2} y^{2} \cdot - 8$

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

Move $y$ .

$- 6 x^{5} y^{5} + 3 x^{4} (y \cdot y) \cdot 3 + 3 x^{3} y \cdot 2 + 3 x^{2} y^{2} \cdot - 8$

Multiply $y$ by $y$ .

$- 6 x^{5} y^{5} + 3 x^{4} y^{2} \cdot 3 + 3 x^{3} y \cdot 2 + 3 x^{2} y^{2} \cdot - 8$

Multiply $3$ by $3$ .

$- 6 x^{5} y^{5} + 9 x^{4} y^{2} + 3 x^{3} y \cdot 2 + 3 x^{2} y^{2} \cdot - 8$

Multiply $2$ by $3$ .

$- 6 x^{5} y^{5} + 9 x^{4} y^{2} + 6 x^{3} y + 3 x^{2} y^{2} \cdot - 8$

Multiply $- 8$ by $3$ .

$- 6 x^{5} y^{5} + 9 x^{4} y^{2} + 6 x^{3} y - 24 x^{2} y^{2}$

Simplify 3x^2y(-2x^3y^4+3x^2y+2x-8y)

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