Basic Math Examples

$(10 y^{7} - 8 y^{6} + 3 y^{4}) \div y^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{10 y^{7} - 8 y^{6} + 3 y^{4}}{y^{2}}$

Step 2

Factor $y^{4}$ out of $10 y^{7} - 8 y^{6} + 3 y^{4}$ .

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Step 2.1

Factor $y^{4}$ out of $10 y^{7}$ .

$\frac{y^{4} (10 y^{3}) - 8 y^{6} + 3 y^{4}}{y^{2}}$

Step 2.2

Factor $y^{4}$ out of $- 8 y^{6}$ .

$\frac{y^{4} (10 y^{3}) + y^{4} (- 8 y^{2}) + 3 y^{4}}{y^{2}}$

Step 2.3

Factor $y^{4}$ out of $3 y^{4}$ .

$\frac{y^{4} (10 y^{3}) + y^{4} (- 8 y^{2}) + y^{4} \cdot 3}{y^{2}}$

Step 2.4

Factor $y^{4}$ out of $y^{4} (10 y^{3}) + y^{4} (- 8 y^{2})$ .

$\frac{y^{4} (10 y^{3} - 8 y^{2}) + y^{4} \cdot 3}{y^{2}}$

Step 2.5

Factor $y^{4}$ out of $y^{4} (10 y^{3} - 8 y^{2}) + y^{4} \cdot 3$ .

$\frac{y^{4} (10 y^{3} - 8 y^{2} + 3)}{y^{2}}$

Step 3

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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Step 3.1

Factor $y^{2}$ out of $y^{4} (10 y^{3} - 8 y^{2} + 3)$ .

$\frac{y^{2} (y^{2} (10 y^{3} - 8 y^{2} + 3))}{y^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{y^{2} (y^{2} (10 y^{3} - 8 y^{2} + 3))}{y^{2} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{y^{2} (y^{2} (10 y^{3} - 8 y^{2} + 3))}{y^{2} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{2} (10 y^{3} - 8 y^{2} + 3)}{1}$

Step 3.2.4

Divide $y^{2} (10 y^{3} - 8 y^{2} + 3)$ by $1$ .

$y^{2} (10 y^{3} - 8 y^{2} + 3)$

Step 4

Apply the distributive property.

$y^{2} (10 y^{3}) + y^{2} (- 8 y^{2}) + y^{2} \cdot 3$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$10 y^{2} y^{3} + y^{2} (- 8 y^{2}) + y^{2} \cdot 3$

Step 5.2

Rewrite using the commutative property of multiplication.

$10 y^{2} y^{3} - 8 y^{2} y^{2} + y^{2} \cdot 3$

Step 5.3

Move $3$ to the left of $y^{2}$ .

$10 y^{2} y^{3} - 8 y^{2} y^{2} + 3 \cdot y^{2}$

Step 6

Simplify each term.

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Step 6.1

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

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Step 6.1.1

Move $y^{3}$ .

$10 (y^{3} y^{2}) - 8 y^{2} y^{2} + 3 \cdot y^{2}$

Step 6.1.2

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

$10 y^{3 + 2} - 8 y^{2} y^{2} + 3 \cdot y^{2}$

Step 6.1.3

Add $3$ and $2$ .

$10 y^{5} - 8 y^{2} y^{2} + 3 \cdot y^{2}$

Step 6.2

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

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Step 6.2.1

Move $y^{2}$ .

$10 y^{5} - 8 (y^{2} y^{2}) + 3 \cdot y^{2}$

Step 6.2.2

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

$10 y^{5} - 8 y^{2 + 2} + 3 \cdot y^{2}$

Step 6.2.3

Add $2$ and $2$ .

$10 y^{5} - 8 y^{4} + 3 \cdot y^{2}$

$10 y^{5} - 8 y^{4} + 3 y^{2}$