Find the Product (2x^3y-3y)^2

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

Rewrite ${(2 x^{3} y - 3 y)}^{2}$ as $(2 x^{3} y - 3 y) (2 x^{3} y - 3 y)$ .

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

Expand $(2 x^{3} y - 3 y) (2 x^{3} y - 3 y)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x^{3}$ .

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

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

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

Add $3$ and $3$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $2$ by $2$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 3$ by $2$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 3$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 3$ by $- 3$ .

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

Subtract $6 y^{2} x^{3}$ from $- 6 x^{3} y^{2}$ .

Move $y^{2}$ .

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

Subtract $6 x^{3} y^{2}$ from $- 6 x^{3} y^{2}$ .

$4 x^{6} y^{2} - 12 x^{3} y^{2} + 9 y^{2}$

Find the Product (2x^3y-3y)^2

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