Simplify -2x^4y^2(6y-xy)

$- 2 x^{4} y^{2} (6 y - x y)$

Step 1

Apply the distributive property.

$- 2 x^{4} y^{2} (6 y) - 2 x^{4} y^{2} (- x y)$

Step 2

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

Move $y$ .

$- 2 x^{4} (y \cdot y^{2}) \cdot 6 - 2 x^{4} y^{2} (- x y)$

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

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

$- 2 x^{4} (y^{1} y^{2}) \cdot 6 - 2 x^{4} y^{2} (- x y)$

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

$- 2 x^{4} y^{1 + 2} \cdot 6 - 2 x^{4} y^{2} (- x y)$

Add $1$ and $2$ .

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

Step 3

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

Move $x$ .

$- 2 x^{4} y^{3} \cdot 6 - 2 (x \cdot x^{4}) y^{2} (- 1 y)$

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

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

$- 2 x^{4} y^{3} \cdot 6 - 2 (x^{1} x^{4}) y^{2} (- 1 y)$

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

$- 2 x^{4} y^{3} \cdot 6 - 2 x^{1 + 4} y^{2} (- 1 y)$

Add $1$ and $4$ .

$- 2 x^{4} y^{3} \cdot 6 - 2 x^{5} y^{2} (- 1 y)$

Step 4

Simplify each term.

Multiply $6$ by $- 2$ .

$- 12 x^{4} y^{3} - 2 x^{5} y^{2} (- 1 y)$

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

Move $y$ .

$- 12 x^{4} y^{3} - 2 x^{5} (y \cdot y^{2}) \cdot - 1$

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

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

$- 12 x^{4} y^{3} - 2 x^{5} (y^{1} y^{2}) \cdot - 1$

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

$- 12 x^{4} y^{3} - 2 x^{5} y^{1 + 2} \cdot - 1$

Add $1$ and $2$ .

$- 12 x^{4} y^{3} - 2 x^{5} y^{3} \cdot - 1$

Multiply $- 1$ by $- 2$ .

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