Basic Math Examples

$3 y (2 y - 5) - 2 (7 y - 5 y^{3})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 y (2 y) + 3 y \cdot - 5 - 2 (7 y - 5 y^{3})$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 \cdot 2 y \cdot y + 3 y \cdot - 5 - 2 (7 y - 5 y^{3})$

Step 1.3

Multiply $- 5$ by $3$ .

$3 \cdot 2 y \cdot y - 15 y - 2 (7 y - 5 y^{3})$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $y$ .

$3 \cdot 2 (y \cdot y) - 15 y - 2 (7 y - 5 y^{3})$

Step 1.4.1.2

Multiply $y$ by $y$ .

$3 \cdot 2 y^{2} - 15 y - 2 (7 y - 5 y^{3})$

Step 1.4.2

Multiply $3$ by $2$ .

$6 y^{2} - 15 y - 2 (7 y - 5 y^{3})$

Step 1.5

Apply the distributive property.

$6 y^{2} - 15 y - 2 (7 y) - 2 (- 5 y^{3})$

Step 1.6

Multiply $7$ by $- 2$ .

$6 y^{2} - 15 y - 14 y - 2 (- 5 y^{3})$

Step 1.7

Multiply $- 5$ by $- 2$ .

$6 y^{2} - 15 y - 14 y + 10 y^{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $14 y$ from $- 15 y$ .

$6 y^{2} - 29 y + 10 y^{3}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $- 29 y$ .

$6 y^{2} + 10 y^{3} - 29 y$

Step 2.2.2

Reorder $6 y^{2}$ and $10 y^{3}$ .

$10 y^{3} + 6 y^{2} - 29 y$