Basic Math Examples

$(- 6 y^{4} + 5 y^{2} + 3 y) (y + 4)$

Step 1

Expand $(- 6 y^{4} + 5 y^{2} + 3 y) (y + 4)$ by multiplying each term in the first expression by each term in the second expression.

$- 6 y^{4} y - 6 y^{4} \cdot 4 + 5 y^{2} y + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $y^{4}$ by $y$ by adding the exponents.

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Step 2.1.1.1

Move $y$ .

$- 6 (y \cdot y^{4}) - 6 y^{4} \cdot 4 + 5 y^{2} y + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.1.2

Multiply $y$ by $y^{4}$ .

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Step 2.1.1.2.1

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

$- 6 (y^{1} y^{4}) - 6 y^{4} \cdot 4 + 5 y^{2} y + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.1.2.2

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

$- 6 y^{1 + 4} - 6 y^{4} \cdot 4 + 5 y^{2} y + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.1.3

Add $1$ and $4$ .

$- 6 y^{5} - 6 y^{4} \cdot 4 + 5 y^{2} y + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.2

Multiply $4$ by $- 6$ .

$- 6 y^{5} - 24 y^{4} + 5 y^{2} y + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.3

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

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Step 2.1.3.1

Move $y$ .

$- 6 y^{5} - 24 y^{4} + 5 (y \cdot y^{2}) + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.3.2

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

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Step 2.1.3.2.1

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

$- 6 y^{5} - 24 y^{4} + 5 (y^{1} y^{2}) + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.3.2.2

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

$- 6 y^{5} - 24 y^{4} + 5 y^{1 + 2} + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.3.3

Add $1$ and $2$ .

$- 6 y^{5} - 24 y^{4} + 5 y^{3} + 5 y^{2} \cdot 4 + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.4

Multiply $4$ by $5$ .

$- 6 y^{5} - 24 y^{4} + 5 y^{3} + 20 y^{2} + 3 y \cdot y + 3 y \cdot 4$

Step 2.1.5

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

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Step 2.1.5.1

Move $y$ .

$- 6 y^{5} - 24 y^{4} + 5 y^{3} + 20 y^{2} + 3 (y \cdot y) + 3 y \cdot 4$

Step 2.1.5.2

Multiply $y$ by $y$ .

$- 6 y^{5} - 24 y^{4} + 5 y^{3} + 20 y^{2} + 3 y^{2} + 3 y \cdot 4$

Step 2.1.6

Multiply $4$ by $3$ .

$- 6 y^{5} - 24 y^{4} + 5 y^{3} + 20 y^{2} + 3 y^{2} + 12 y$

Step 2.2

Add $20 y^{2}$ and $3 y^{2}$ .

$- 6 y^{5} - 24 y^{4} + 5 y^{3} + 23 y^{2} + 12 y$