Simplify -3xy(4x^2y^4-2xy^3)

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

Step 1

Apply the distributive property.

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

Step 2

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Step 3

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Step 4

Simplify each term.

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

Move $y^{4}$ .

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

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

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

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

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

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

Add $4$ and $1$ .

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

Multiply $4$ by $- 3$ .

$- 12 x^{3} y^{5} - 3 x^{2} y (- 2 y^{3})$

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

Move $y^{3}$ .

$- 12 x^{3} y^{5} - 3 x^{2} (y^{3} y) \cdot - 2$

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

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

$- 12 x^{3} y^{5} - 3 x^{2} (y^{3} y^{1}) \cdot - 2$

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

$- 12 x^{3} y^{5} - 3 x^{2} y^{3 + 1} \cdot - 2$

Add $3$ and $1$ .

$- 12 x^{3} y^{5} - 3 x^{2} y^{4} \cdot - 2$

Multiply $- 2$ by $- 3$ .

$- 12 x^{3} y^{5} + 6 x^{2} y^{4}$

Simplify -3xy(4x^2y^4-2xy^3)

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