Basic Math Examples

$6 y (2 y^{2} - 4) - y (8 y)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$6 y (2 y^{2}) + 6 y \cdot - 4 - y (8 y)$

Step 1.2

Rewrite using the commutative property of multiplication.

$6 \cdot 2 y \cdot y^{2} + 6 y \cdot - 4 - y (8 y)$

Step 1.3

Multiply $- 4$ by $6$ .

$6 \cdot 2 y \cdot y^{2} - 24 y - y (8 y)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $y^{2}$ .

$6 \cdot 2 (y^{2} y) - 24 y - y (8 y)$

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

$6 \cdot 2 (y^{2} y^{1}) - 24 y - y (8 y)$

Step 1.4.1.2.2

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

$6 \cdot 2 y^{2 + 1} - 24 y - y (8 y)$

Step 1.4.1.3

Add $2$ and $1$ .

$6 \cdot 2 y^{3} - 24 y - y (8 y)$

Step 1.4.2

Multiply $6$ by $2$ .

$12 y^{3} - 24 y - y (8 y)$

Step 1.5

Rewrite using the commutative property of multiplication.

$12 y^{3} - 24 y - 1 \cdot 8 y \cdot y$

Step 1.6

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

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Step 1.6.1

Move $y$ .

$12 y^{3} - 24 y - 1 \cdot 8 (y \cdot y)$

Step 1.6.2

Multiply $y$ by $y$ .

$12 y^{3} - 24 y - 1 \cdot 8 y^{2}$

Step 1.7

Multiply $- 1$ by $8$ .

$12 y^{3} - 24 y - 8 y^{2}$

Step 2

Move $- 24 y$ .

$12 y^{3} - 8 y^{2} - 24 y$