Pre-Algebra Examples

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

Step 1

Factor $2 x$ out of $4 x y^{2} (3 y - x) - 2 x^{2} {(x - 3 y)}^{2}$ .

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Step 1.1

Factor $2 x$ out of $4 x y^{2} (3 y - x)$ .

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

Step 1.2

Factor $2 x$ out of $- 2 x^{2} {(x - 3 y)}^{2}$ .

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

Step 1.3

Factor $2 x$ out of $2 x (2 y^{2} (3 y - x)) + 2 x (- x {(x - 3 y)}^{2})$ .

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

Step 2

Apply the distributive property.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Rewrite using the commutative property of multiplication.

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

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

Move $y$ .

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

Step 5.1.2

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

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Step 5.1.2.1

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

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

Step 5.1.2.2

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

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

Step 5.1.3

Add $1$ and $2$ .

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

Step 5.2

Multiply $2$ by $3$ .

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

Step 5.3

Multiply $2$ by $- 1$ .

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

Step 6

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

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

Step 7

Expand $(x - 3 y) (x - 3 y)$ using the FOIL Method.

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Step 7.1

Apply the distributive property.

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

Step 7.2

Apply the distributive property.

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

Step 7.3

Apply the distributive property.

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

Step 8

Simplify and combine like terms.

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Step 8.1

Simplify each term.

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Step 8.1.1

Multiply $x$ by $x$ .

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

Step 8.1.2

Rewrite using the commutative property of multiplication.

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

Step 8.1.3

Rewrite using the commutative property of multiplication.

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

Step 8.1.4

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

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Step 8.1.4.1

Move $y$ .

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

Step 8.1.4.2

Multiply $y$ by $y$ .

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

Step 8.1.5

Multiply $- 3$ by $- 3$ .

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

Step 8.2

Subtract $3 y x$ from $- 3 x y$ .

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Step 8.2.1

Move $y$ .

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

Step 8.2.2

Subtract $3 x y$ from $- 3 x y$ .

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

Step 9

Apply the distributive property.

$2 x (6 y^{3} - 2 y^{2} x - x \cdot x^{2} - x (- 6 x y) - x (9 y^{2}))$

Step 10

Simplify.

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Step 10.1

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

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Step 10.1.1

Move $x^{2}$ .

$2 x (6 y^{3} - 2 y^{2} x - (x^{2} x) - x (- 6 x y) - x (9 y^{2}))$

Step 10.1.2

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

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Step 10.1.2.1

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

$2 x (6 y^{3} - 2 y^{2} x - (x^{2} x^{1}) - x (- 6 x y) - x (9 y^{2}))$

Step 10.1.2.2

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

$2 x (6 y^{3} - 2 y^{2} x - x^{2 + 1} - x (- 6 x y) - x (9 y^{2}))$

Step 10.1.3

Add $2$ and $1$ .

$2 x (6 y^{3} - 2 y^{2} x - x^{3} - x (- 6 x y) - x (9 y^{2}))$

Step 10.2

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

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Step 10.2.1

Move $x$ .

$2 x (6 y^{3} - 2 y^{2} x - x^{3} - (x \cdot x) (- 6 y) - x (9 y^{2}))$

Step 10.2.2

Multiply $x$ by $x$ .

$2 x (6 y^{3} - 2 y^{2} x - x^{3} - x^{2} (- 6 y) - x (9 y^{2}))$

Step 10.3

Rewrite using the commutative property of multiplication.

$2 x (6 y^{3} - 2 y^{2} x - x^{3} - x^{2} (- 6 y) - 1 \cdot 9 x y^{2})$

Step 11

Simplify each term.

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Step 11.1

Rewrite using the commutative property of multiplication.

$2 x (6 y^{3} - 2 y^{2} x - x^{3} - 1 \cdot - 6 x^{2} y - 1 \cdot 9 x y^{2})$

Step 11.2

Multiply $- 1$ by $- 6$ .

$2 x (6 y^{3} - 2 y^{2} x - x^{3} + 6 x^{2} y - 1 \cdot 9 x y^{2})$

Step 11.3

Multiply $- 1$ by $9$ .

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

Step 12

Subtract $9 x y^{2}$ from $- 2 y^{2} x$ .

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Step 12.1

Move $y^{2}$ .

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

Step 12.2

Subtract $9 x y^{2}$ from $- 2 x y^{2}$ .

$2 x (6 y^{3} - x^{3} + 6 x^{2} y - 11 x y^{2})$