Basic Math Examples

$\frac{0.075 y^{2} + 0.615 y + 1.2}{y + 5}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $0.015$ out of $0.075 y^{2} + 0.615 y + 1.2$ .

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Step 1.1.1

Factor $0.015$ out of $0.075 y^{2}$ .

$\frac{0.015 (5 y^{2}) + 0.615 y + 1.2}{y + 5}$

Step 1.1.2

Factor $0.015$ out of $0.615 y$ .

$\frac{0.015 (5 y^{2}) + 0.015 (41 y) + 1.2}{y + 5}$

Step 1.1.3

Factor $0.015$ out of $1.2$ .

$\frac{0.015 (5 y^{2}) + 0.015 (41 y) + 0.015 (80)}{y + 5}$

Step 1.1.4

Factor $0.015$ out of $0.015 (5 y^{2}) + 0.015 (41 y)$ .

$\frac{0.015 (5 y^{2} + 41 y) + 0.015 (80)}{y + 5}$

Step 1.1.5

Factor $0.015$ out of $0.015 (5 y^{2} + 41 y) + 0.015 (80)$ .

$\frac{0.015 (5 y^{2} + 41 y + 80)}{y + 5}$

Step 1.2

Factor by grouping.

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Step 1.2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot 80 = 400$ and whose sum is $b = 41$ .

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Step 1.2.1.1

Factor $41$ out of $41 y$ .

$\frac{0.015 (5 y^{2} + 41 (y) + 80)}{y + 5}$

Step 1.2.1.2

Rewrite $41$ as $16$ plus $25$

$\frac{0.015 (5 y^{2} + (16 + 25) y + 80)}{y + 5}$

Step 1.2.1.3

Apply the distributive property.

$\frac{0.015 (5 y^{2} + 16 y + 25 y + 80)}{y + 5}$

Step 1.2.2

Factor out the greatest common factor from each group.

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Step 1.2.2.1

Group the first two terms and the last two terms.

$\frac{0.015 ((5 y^{2} + 16 y) + 25 y + 80)}{y + 5}$

Step 1.2.2.2

Factor out the greatest common factor (GCF) from each group.

$\frac{0.015 (y (5 y + 16) + 5 (5 y + 16))}{y + 5}$

Step 1.2.3

Factor the polynomial by factoring out the greatest common factor, $5 y + 16$ .

$\frac{0.015 ((5 y + 16) (y + 5))}{y + 5}$

$\frac{0.015 (5 y + 16) (y + 5)}{y + 5}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $y + 5$ .

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Step 2.1.1

Cancel the common factor.

$\frac{0.015 (5 y + 16) (y + 5)}{y + 5}$

Step 2.1.2

Divide $0.015 (5 y + 16)$ by $1$ .

$0.015 (5 y + 16)$

Step 2.2

Apply the distributive property.

$0.015 (5 y) + 0.015 \cdot 16$

Step 2.3

Multiply.

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Step 2.3.1

Multiply $5$ by $0.015$ .

$0.075 y + 0.015 \cdot 16$

Step 2.3.2

Multiply $0.015$ by $16$ .

$0.075 y + 0.24$