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

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

Step 1

Apply the distributive property.

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

Step 2

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Step 3

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Step 4

Simplify each term.

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $3$ by $- 4$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 4$ by $- 4$ .

$- 12 x^{3} y^{3} + 16 x^{3} y^{2}$

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

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