Basic Math Examples

$(2 y^{5} - 3 y^{3} + 8) \cdot (5 y^{2})$

Step 1

Apply the distributive property.

$2 y^{5} (5 y^{2}) - 3 y^{3} (5 y^{2}) + 8 (5 y^{2})$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 5 y^{5} y^{2} - 3 y^{3} (5 y^{2}) + 8 (5 y^{2})$

Step 2.2

Rewrite using the commutative property of multiplication.

$2 \cdot 5 y^{5} y^{2} - 3 \cdot 5 y^{3} y^{2} + 8 (5 y^{2})$

Step 2.3

Multiply $5$ by $8$ .

$2 \cdot 5 y^{5} y^{2} - 3 \cdot 5 y^{3} y^{2} + 40 y^{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $y^{5}$ by $y^{2}$ by adding the exponents.

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Step 3.1.1

Move $y^{2}$ .

$2 \cdot 5 (y^{2} y^{5}) - 3 \cdot 5 y^{3} y^{2} + 40 y^{2}$

Step 3.1.2

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

$2 \cdot 5 y^{2 + 5} - 3 \cdot 5 y^{3} y^{2} + 40 y^{2}$

Step 3.1.3

Add $2$ and $5$ .

$2 \cdot 5 y^{7} - 3 \cdot 5 y^{3} y^{2} + 40 y^{2}$

Step 3.2

Multiply $2$ by $5$ .

$10 y^{7} - 3 \cdot 5 y^{3} y^{2} + 40 y^{2}$

Step 3.3

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

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Step 3.3.1

Move $y^{2}$ .

$10 y^{7} - 3 \cdot 5 (y^{2} y^{3}) + 40 y^{2}$

Step 3.3.2

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

$10 y^{7} - 3 \cdot 5 y^{2 + 3} + 40 y^{2}$

Step 3.3.3

Add $2$ and $3$ .

$10 y^{7} - 3 \cdot 5 y^{5} + 40 y^{2}$

Step 3.4

Multiply $- 3$ by $5$ .

$10 y^{7} - 15 y^{5} + 40 y^{2}$