Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $y$ .

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

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

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

Step 2.1.2.2.2

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

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

Step 2.1.2.3

Add $1$ and $2$ .

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

Step 2.1.3

Move $2$ to the left of $y^{2}$ .

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

$2 y^{3} + 2 y^{2} - 3 \cdot 2 y \cdot y - 3 y \cdot 2$

Step 2.1.5

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

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Step 2.1.5.1

Move $y$ .

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

Step 2.1.5.2

Multiply $y$ by $y$ .

$2 y^{3} + 2 y^{2} - 3 \cdot 2 y^{2} - 3 y \cdot 2$

Step 2.1.6

Multiply $- 3$ by $2$ .

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

Step 2.1.7

Multiply $2$ by $- 3$ .

$2 y^{3} + 2 y^{2} - 6 y^{2} - 6 y$

Step 2.2

Subtract $6 y^{2}$ from $2 y^{2}$ .

$2 y^{3} - 4 y^{2} - 6 y$