Basic Math Examples

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

Step 1

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

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Step 1.1

Move $y$ .

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

Step 1.2

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

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Step 1.2.1

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

$4 y (2 (y^{1} y^{2}) - 3 y) - 3 y^{2 (y - 4)}$

Step 1.2.2

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

$4 y (2 y^{1 + 2} - 3 y) - 3 y^{2 (y - 4)}$

Step 1.3

Add $1$ and $2$ .

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

Step 2

Apply the distributive property.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Rewrite using the commutative property of multiplication.

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

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

Move $y^{3}$ .

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

Step 5.1.2

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

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Step 5.1.2.1

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

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

Step 5.1.2.2

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

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

Step 5.1.3

Add $3$ and $1$ .

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

Step 5.2

Multiply $4$ by $2$ .

$8 y^{4} + 4 \cdot - 3 y \cdot y - 3 y^{2 (y - 4)}$

Step 5.3

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

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Step 5.3.1

Move $y$ .

$8 y^{4} + 4 \cdot - 3 (y \cdot y) - 3 y^{2 (y - 4)}$

Step 5.3.2

Multiply $y$ by $y$ .

$8 y^{4} + 4 \cdot - 3 y^{2} - 3 y^{2 (y - 4)}$

Step 5.4

Multiply $4$ by $- 3$ .

$8 y^{4} - 12 y^{2} - 3 y^{2 (y - 4)}$

Step 6

Apply the distributive property.

$8 y^{4} - 12 y^{2} - 3 y^{2 y + 2 \cdot - 4}$

Step 7

Multiply $2$ by $- 4$ .

$8 y^{4} - 12 y^{2} - 3 y^{2 y - 8}$