Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $3 x^{2} y (3 x^{2} y) + 3 x^{2} y (2 x y) - 2 x y (3 x^{2} y) - 2 x y (2 x y)$ .

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Step 2.1.1

Reorder the factors in the terms $3 x^{2} y (2 x y)$ and $- 2 x y (3 x^{2} y)$ .

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

Step 2.1.2

Subtract $2 \cdot 3 x^{2} x y \cdot y$ from $2 \cdot 3 x^{2} x y \cdot y$ .

$3 x^{2} y (3 x^{2} y) + 0 - 2 x y (2 x y)$

Step 2.1.3

Add $3 x^{2} y (3 x^{2} y)$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

Move $x^{2}$ .

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

Step 2.2.1.2

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

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

Step 2.2.1.3

Add $2$ and $2$ .

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

Step 2.2.2

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

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Step 2.2.2.1

Move $y$ .

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

Step 2.2.2.2

Multiply $y$ by $y$ .

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

Step 2.2.3

Multiply $3$ by $3$ .

$9 x^{4} y^{2} - 2 x y (2 x y)$

Step 2.2.4

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

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Step 2.2.4.1

Move $x$ .

$9 x^{4} y^{2} - 2 (x \cdot x) y (2 y)$

Step 2.2.4.2

Multiply $x$ by $x$ .

$9 x^{4} y^{2} - 2 x^{2} y (2 y)$

Step 2.2.5

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

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Step 2.2.5.1

Move $y$ .

$9 x^{4} y^{2} - 2 x^{2} (y \cdot y) \cdot 2$

Step 2.2.5.2

Multiply $y$ by $y$ .

$9 x^{4} y^{2} - 2 x^{2} y^{2} \cdot 2$

Step 2.2.6

Multiply $2$ by $- 2$ .

$9 x^{4} y^{2} - 4 x^{2} y^{2}$