Combine 1/400(a^2)-(0.2*a)-15

$\frac{1}{400} (a^{2}) - (0.2 \cdot a) - 15$

Step 1

Simplify each term.

Combine $\frac{1}{400}$ and $a^{2}$ .

$\frac{a^{2}}{400} - (0.2 \cdot a) - 15$

Multiply $0.2$ by $- 1$ .

$\frac{a^{2}}{400} - 0.2 a - 15$

Step 2

To write $- 0.2 a$ as a fraction with a common denominator, multiply by $\frac{400}{400}$ .

$\frac{a^{2}}{400} - 0.2 a \cdot \frac{400}{400} - 15$

Step 3

Simplify terms.

Combine $- 0.2 a$ and $\frac{400}{400}$ .

$\frac{a^{2}}{400} + \frac{- 0.2 a \cdot 400}{400} - 15$

Combine the numerators over the common denominator.

$\frac{a^{2} - 0.2 a \cdot 400}{400} - 15$

Step 4

Simplify the numerator.

Factor $a$ out of $a^{2} - 0.2 a \cdot 400$ .

Factor $a$ out of $a^{2}$ .

$\frac{a \cdot a - 0.2 a \cdot 400}{400} - 15$

Factor $a$ out of $- 0.2 a \cdot 400$ .

$\frac{a \cdot a + a (- 0.2 \cdot 400)}{400} - 15$

Factor $a$ out of $a \cdot a + a (- 0.2 \cdot 400)$ .

$\frac{a (a - 0.2 \cdot 400)}{400} - 15$

Multiply $- 0.2$ by $400$ .

$\frac{a (a - 80)}{400} - 15$

Step 5

To write $- 15$ as a fraction with a common denominator, multiply by $\frac{400}{400}$ .

$\frac{a (a - 80)}{400} - 15 \cdot \frac{400}{400}$

Step 6

Simplify terms.

Combine $- 15$ and $\frac{400}{400}$ .

$\frac{a (a - 80)}{400} + \frac{- 15 \cdot 400}{400}$

Combine the numerators over the common denominator.

$\frac{a (a - 80) - 15 \cdot 400}{400}$

Step 7

Simplify the numerator.

Apply the distributive property.

$\frac{a \cdot a + a \cdot - 80 - 15 \cdot 400}{400}$

Multiply $a$ by $a$ .

$\frac{a^{2} + a \cdot - 80 - 15 \cdot 400}{400}$

Move $- 80$ to the left of $a$ .

$\frac{a^{2} - 80 \cdot a - 15 \cdot 400}{400}$

Multiply $- 15$ by $400$ .

$\frac{a^{2} - 80 a - 6000}{400}$