Algebra Examples

$- 2 x y (9 x y^{3} - 7 x y + 4 y^{2})$

Step 1

Apply the distributive property.

$- 2 x y (9 x y^{3}) - 2 x y (- 7 x y) - 2 x y (4 y^{2})$

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

$- 2 (x \cdot x) y (9 y^{3}) - 2 x y (- 7 x y) - 2 x y (4 y^{2})$

Step 2.1.2

Multiply $x$ by $x$ .

$- 2 x^{2} y (9 y^{3}) - 2 x y (- 7 x y) - 2 x y (4 y^{2})$

Step 2.2

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

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Step 2.2.1

Move $x$ .

$- 2 x^{2} y (9 y^{3}) - 2 (x \cdot x) y (- 7 y) - 2 x y (4 y^{2})$

Step 2.2.2

Multiply $x$ by $x$ .

$- 2 x^{2} y (9 y^{3}) - 2 x^{2} y (- 7 y) - 2 x y (4 y^{2})$

Step 2.3

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

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Step 2.3.1

Move $y^{2}$ .

$- 2 x^{2} y (9 y^{3}) - 2 x^{2} y (- 7 y) - 2 x (y^{2} y) \cdot 4$

Step 2.3.2

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

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Step 2.3.2.1

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

$- 2 x^{2} y (9 y^{3}) - 2 x^{2} y (- 7 y) - 2 x (y^{2} y^{1}) \cdot 4$

Step 2.3.2.2

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

$- 2 x^{2} y (9 y^{3}) - 2 x^{2} y (- 7 y) - 2 x y^{2 + 1} \cdot 4$

Step 2.3.3

Add $2$ and $1$ .

$- 2 x^{2} y (9 y^{3}) - 2 x^{2} y (- 7 y) - 2 x y^{3} \cdot 4$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $y^{3}$ .

$- 2 x^{2} (y^{3} y) \cdot 9 - 2 x^{2} y (- 7 y) - 2 x y^{3} \cdot 4$

Step 3.1.2

Multiply $y^{3}$ by $y$ .

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Step 3.1.2.1

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

$- 2 x^{2} (y^{3} y^{1}) \cdot 9 - 2 x^{2} y (- 7 y) - 2 x y^{3} \cdot 4$

Step 3.1.2.2

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

$- 2 x^{2} y^{3 + 1} \cdot 9 - 2 x^{2} y (- 7 y) - 2 x y^{3} \cdot 4$

Step 3.1.3

Add $3$ and $1$ .

$- 2 x^{2} y^{4} \cdot 9 - 2 x^{2} y (- 7 y) - 2 x y^{3} \cdot 4$

Step 3.2

Multiply $9$ by $- 2$ .

$- 18 x^{2} y^{4} - 2 x^{2} y (- 7 y) - 2 x y^{3} \cdot 4$

Step 3.3

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

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Step 3.3.1

Move $y$ .

$- 18 x^{2} y^{4} - 2 x^{2} (y \cdot y) \cdot - 7 - 2 x y^{3} \cdot 4$

Step 3.3.2

Multiply $y$ by $y$ .

$- 18 x^{2} y^{4} - 2 x^{2} y^{2} \cdot - 7 - 2 x y^{3} \cdot 4$

Step 3.4

Multiply $- 7$ by $- 2$ .

$- 18 x^{2} y^{4} + 14 x^{2} y^{2} - 2 x y^{3} \cdot 4$

Step 3.5

Multiply $4$ by $- 2$ .

$- 18 x^{2} y^{4} + 14 x^{2} y^{2} - 8 x y^{3}$