Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

Move $x^{3}$ .

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

Step 3.1.1.2

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

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

Step 3.1.1.3

Add $3$ and $3$ .

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

Step 3.1.2

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

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Step 3.1.2.1

Move $y$ .

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

Step 3.1.2.2

Multiply $y$ by $y$ .

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

Step 3.1.3

Multiply $2$ by $2$ .

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

Step 3.1.4

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

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Step 3.1.4.1

Move $y$ .

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

Step 3.1.4.2

Multiply $y$ by $y$ .

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

Step 3.1.5

Multiply $- 3$ by $2$ .

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

Step 3.1.6

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

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Step 3.1.6.1

Move $y$ .

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

Step 3.1.6.2

Multiply $y$ by $y$ .

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

Step 3.1.7

Rewrite using the commutative property of multiplication.

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

Step 3.1.8

Multiply $- 3$ by $2$ .

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

Step 3.1.9

Rewrite using the commutative property of multiplication.

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

Step 3.1.10

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

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Step 3.1.10.1

Move $y$ .

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

Step 3.1.10.2

Multiply $y$ by $y$ .

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

Step 3.1.11

Multiply $- 3$ by $- 3$ .

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

Step 3.2

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

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Step 3.2.1

Move $y^{2}$ .

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

Step 3.2.2

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

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