Basic Math Examples

$- (3 y - 5) (4 - y^{2})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$(- (3 y) - - 5) (4 - y^{2})$

Step 1.2

Multiply.

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Step 1.2.1

Multiply $3$ by $- 1$ .

$(- 3 y - - 5) (4 - y^{2})$

Step 1.2.2

Multiply $- 1$ by $- 5$ .

$(- 3 y + 5) (4 - y^{2})$

Step 2

Expand $(- 3 y + 5) (4 - y^{2})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- 3 y (4 - y^{2}) + 5 (4 - y^{2})$

Step 2.2

Apply the distributive property.

$- 3 y \cdot 4 - 3 y (- y^{2}) + 5 (4 - y^{2})$

Step 2.3

Apply the distributive property.

$- 3 y \cdot 4 - 3 y (- y^{2}) + 5 \cdot 4 + 5 (- y^{2})$

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $4$ by $- 3$ .

$- 12 y - 3 y (- y^{2}) + 5 \cdot 4 + 5 (- y^{2})$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$- 12 y - 3 \cdot - 1 y \cdot y^{2} + 5 \cdot 4 + 5 (- y^{2})$

Step 3.1.3

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

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Step 3.1.3.1

Move $y^{2}$ .

$- 12 y - 3 \cdot - 1 (y^{2} y) + 5 \cdot 4 + 5 (- y^{2})$

Step 3.1.3.2

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

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Step 3.1.3.2.1

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

$- 12 y - 3 \cdot - 1 (y^{2} y^{1}) + 5 \cdot 4 + 5 (- y^{2})$

Step 3.1.3.2.2

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

$- 12 y - 3 \cdot - 1 y^{2 + 1} + 5 \cdot 4 + 5 (- y^{2})$

Step 3.1.3.3

Add $2$ and $1$ .

$- 12 y - 3 \cdot - 1 y^{3} + 5 \cdot 4 + 5 (- y^{2})$

Step 3.1.4

Multiply $- 3$ by $- 1$ .

$- 12 y + 3 y^{3} + 5 \cdot 4 + 5 (- y^{2})$

Step 3.1.5

Multiply $5$ by $4$ .

$- 12 y + 3 y^{3} + 20 + 5 (- y^{2})$

Step 3.1.6

Multiply $- 1$ by $5$ .

$- 12 y + 3 y^{3} + 20 - 5 y^{2}$

Step 3.2

Reorder.

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Step 3.2.1

Move $20$ .

$- 12 y + 3 y^{3} - 5 y^{2} + 20$

Step 3.2.2

Move $- 12 y$ .

$3 y^{3} - 5 y^{2} - 12 y + 20$