Question

Which expression is equal to c² - 46c * 15c³ / c² * 4c / 12c³ * 30c²?

a) 15
b) c² - 46c
c) -15
d) c² + 46c

Answer 1

The expression is equal to -15.

1. Given expression:
`\( (c^2 - 46c \cdot 15c^3)/(c^2 \cdot 4c) / (12c^3 \cdot 30c^2)/(1) \)`.

2. Simplifying the expression involves canceling out common factors:

`\[ ((c \cdot (c - 46 \cdot 15c^2)))/((c \cdot 4) / (12 \cdot 30c)) \]`

3. Further simplifying:

`\[ ((c \cdot (c - 690c^2)))/((4) / (360c)) \]`

4. Simplifying the numerator and denominator:

`\[ (c^2 - 690c^3)/(90c) \]`

5. Factoring out common factor c from the numerator:

`\[ (c \cdot (c - 690c^2))/(90c) \]`

6. Canceling out common factors:

`\[ (c - 690c^2)/(90) \]`

7. Factoring out common factor c from the numerator:

`\[ (c \cdot (1 - 690c))/(90) \]`

8. Simplifying further:

`\[ (-690c^2 + c)/(90) = (c(1 - 690c))/(90) \]`

9. Simplifying:

`\[ (-690c^2 + c)/(90) = -(690c^2 - c)/(90) = -(c(690c^2 - 1))/(90) \]`

10. Further simplifying, we get:

`\[ -(c(690c^2 - 1))/(90) = -(c(26c + 1)(26c - 1))/(90) \]`

11. Canceling out common factors:

`\[ -((26c + 1)(26c - 1))/(90) \]`

12. This is equivalent to -15.

Therefore, the correct answer is (c) -15.