Basic Math Examples

$\frac{- 49 y^{6} + 14 y^{4} - 28 y^{5}}{- 7 y^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $7 y^{4}$ out of $- 49 y^{6} + 14 y^{4} - 28 y^{5}$ .

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Step 1.1.1

Factor $7 y^{4}$ out of $- 49 y^{6}$ .

$\frac{7 y^{4} (- 7 y^{2}) + 14 y^{4} - 28 y^{5}}{- 7 y^{2}}$

Step 1.1.2

Factor $7 y^{4}$ out of $14 y^{4}$ .

$\frac{7 y^{4} (- 7 y^{2}) + 7 y^{4} (2) - 28 y^{5}}{- 7 y^{2}}$

Step 1.1.3

Factor $7 y^{4}$ out of $- 28 y^{5}$ .

$\frac{7 y^{4} (- 7 y^{2}) + 7 y^{4} (2) + 7 y^{4} (- 4 y)}{- 7 y^{2}}$

Step 1.1.4

Factor $7 y^{4}$ out of $7 y^{4} (- 7 y^{2}) + 7 y^{4} (2)$ .

$\frac{7 y^{4} (- 7 y^{2} + 2) + 7 y^{4} (- 4 y)}{- 7 y^{2}}$

Step 1.1.5

Factor $7 y^{4}$ out of $7 y^{4} (- 7 y^{2} + 2) + 7 y^{4} (- 4 y)$ .

$\frac{7 y^{4} (- 7 y^{2} + 2 - 4 y)}{- 7 y^{2}}$

Step 1.2

Reorder terms.

$\frac{7 y^{4} (- 7 y^{2} - 4 y + 2)}{- 7 y^{2}}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $7$ and $- 7$ .

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Step 2.1.1

Factor $7$ out of $7 y^{4} (- 7 y^{2} - 4 y + 2)$ .

$\frac{7 (y^{4} (- 7 y^{2} - 4 y + 2))}{- 7 y^{2}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $7$ out of $- 7 y^{2}$ .

$\frac{7 (y^{4} (- 7 y^{2} - 4 y + 2))}{7 (- y^{2})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{7 (y^{4} (- 7 y^{2} - 4 y + 2))}{7 (- y^{2})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{y^{4} (- 7 y^{2} - 4 y + 2)}{- y^{2}}$

Step 2.2

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

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Step 2.2.1

Factor $y^{2}$ out of $y^{4} (- 7 y^{2} - 4 y + 2)$ .

$\frac{y^{2} (y^{2} (- 7 y^{2} - 4 y + 2))}{- y^{2}}$

Step 2.2.2

Move the negative one from the denominator of $\frac{y^{2} (- 7 y^{2} - 4 y + 2)}{- 1}$ .

$- 1 \cdot (y^{2} (- 7 y^{2} - 4 y + 2))$

Step 2.3

Rewrite $- 1 \cdot (y^{2} (- 7 y^{2} - 4 y + 2))$ as $- (y^{2} (- 7 y^{2} - 4 y + 2))$ .

$- (y^{2} (- 7 y^{2} - 4 y + 2))$

Step 2.4

Apply the distributive property.

$- (y^{2} (- 7 y^{2}) + y^{2} (- 4 y) + y^{2} \cdot 2)$

Step 3

Simplify.

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Step 3.1

Rewrite using the commutative property of multiplication.

$- (- 7 y^{2} y^{2} + y^{2} (- 4 y) + y^{2} \cdot 2)$

Step 3.2

Rewrite using the commutative property of multiplication.

$- (- 7 y^{2} y^{2} - 4 y^{2} y + y^{2} \cdot 2)$

Step 3.3

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

$- (- 7 y^{2} y^{2} - 4 y^{2} y + 2 \cdot y^{2})$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $y^{2}$ .

$- (- 7 (y^{2} y^{2}) - 4 y^{2} y + 2 \cdot y^{2})$

Step 4.1.2

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

$- (- 7 y^{2 + 2} - 4 y^{2} y + 2 \cdot y^{2})$

Step 4.1.3

Add $2$ and $2$ .

$- (- 7 y^{4} - 4 y^{2} y + 2 \cdot y^{2})$

Step 4.2

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

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Step 4.2.1

Move $y$ .

$- (- 7 y^{4} - 4 (y \cdot y^{2}) + 2 \cdot y^{2})$

Step 4.2.2

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

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Step 4.2.2.1

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

$- (- 7 y^{4} - 4 (y^{1} y^{2}) + 2 \cdot y^{2})$

Step 4.2.2.2

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

$- (- 7 y^{4} - 4 y^{1 + 2} + 2 \cdot y^{2})$

Step 4.2.3

Add $1$ and $2$ .

$- (- 7 y^{4} - 4 y^{3} + 2 \cdot y^{2})$

$- (- 7 y^{4} - 4 y^{3} + 2 y^{2})$

Step 5

Apply the distributive property.

$- (- 7 y^{4}) - (- 4 y^{3}) - (2 y^{2})$

Step 6

Simplify.

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Step 6.1

Multiply $- 7$ by $- 1$ .

$7 y^{4} - (- 4 y^{3}) - (2 y^{2})$

Step 6.2

Multiply $- 4$ by $- 1$ .

$7 y^{4} + 4 y^{3} - (2 y^{2})$

Step 6.3

Multiply $2$ by $- 1$ .

$7 y^{4} + 4 y^{3} - 2 y^{2}$