Simplify (2x-3xy)(xy^2+2xy-3x)

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

Expand $(2 x - 3 x y) (x y^{2} + 2 x y - 3 x)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 3$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $2$ by $- 3$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $- 3$ .

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

Simplify by adding terms.

Subtract $6 x^{2} y^{2}$ from $2 x^{2} y^{2}$ .

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

Add $4 x^{2} y$ and $9 x^{2} y$ .

$- 6 x^{2} - 3 x^{2} y^{3} - 4 x^{2} y^{2} + 13 x^{2} y$

Simplify (2x-3xy)(xy^2+2xy-3x)

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