Basic Math Examples

$\frac{14 y^{7} + 2 y^{6}}{y}$

Step 1

Simplify terms.

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Step 1.1

Factor $2 y^{6}$ out of $14 y^{7} + 2 y^{6}$ .

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Step 1.1.1

Factor $2 y^{6}$ out of $14 y^{7}$ .

$\frac{2 y^{6} (7 y) + 2 y^{6}}{y}$

Step 1.1.2

Factor $2 y^{6}$ out of $2 y^{6}$ .

$\frac{2 y^{6} (7 y) + 2 y^{6} (1)}{y}$

Step 1.1.3

Factor $2 y^{6}$ out of $2 y^{6} (7 y) + 2 y^{6} (1)$ .

$\frac{2 y^{6} (7 y + 1)}{y}$

Step 1.2

Cancel the common factor of $y^{6}$ and $y$ .

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Step 1.2.1

Factor $y$ out of $2 y^{6} (7 y + 1)$ .

$\frac{y (2 y^{5} (7 y + 1))}{y}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

$\frac{y (2 y^{5} (7 y + 1))}{y^{1}}$

Step 1.2.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (2 y^{5} (7 y + 1))}{y \cdot 1}$

Step 1.2.2.3

Cancel the common factor.

$\frac{y (2 y^{5} (7 y + 1))}{y \cdot 1}$

Step 1.2.2.4

Rewrite the expression.

$\frac{2 y^{5} (7 y + 1)}{1}$

Step 1.2.2.5

Divide $2 y^{5} (7 y + 1)$ by $1$ .

$2 y^{5} (7 y + 1)$

Step 1.3

Apply the distributive property.

$2 y^{5} (7 y) + 2 y^{5} \cdot 1$

Step 1.4

Simplify the expression.

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Step 1.4.1

Rewrite using the commutative property of multiplication.

$2 \cdot 7 y^{5} y + 2 y^{5} \cdot 1$

Step 1.4.2

Multiply $2$ by $1$ .

$2 \cdot 7 y^{5} y + 2 y^{5}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $y$ .

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

Step 2.1.2

Multiply $y$ by $y^{5}$ .

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Step 2.1.2.1

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

$2 \cdot 7 (y^{1} y^{5}) + 2 y^{5}$

Step 2.1.2.2

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

$2 \cdot 7 y^{1 + 5} + 2 y^{5}$

Step 2.1.3

Add $1$ and $5$ .

$2 \cdot 7 y^{6} + 2 y^{5}$

Step 2.2

Multiply $2$ by $7$ .

$14 y^{6} + 2 y^{5}$