F(x) = -2(x - 3)² + 2
f(x) = -2(x - 3)(x - 3) + 2
f(x) = -2[x(x - 3) - 3(x - 3)] + 2
f(x) = -2[x(x) - x(3) - 3(x) - 3(-3)] + 2
f(x) = -2(x² - 3x - 3x + 9) + 2
f(x) = -2(x² - 6x + 9) + 2
f(x) = -2(x²) - 2(-6x) - 2(9) + 2
f(x) = -2x² + 12x - 18 + 2
f(x) = -2x² + 12x - 16
Answer:
6x² + 5x - 6
Step-by-step explanation:
Given
(2x + 3)(3x - 2)
Each term in the second factor is multiplied by each term in the first factor, that is
2x(3x - 2) + 3(3x - 2) ← distribute both parenthesis
= 6x² - 4x + 9x - 6 ← collect like terms
= 6x² + 5x - 6
36 actually, I counted it myself
Answer:
The simplest form is tan(4x)
Step-by-step explanation:
* Lets revise the identity of the compound angles
- 
- 
* Lets solve the problem
- Let 9x = 5x + 4x
∴ tan(9x) = tan(5x + 4x)
- Use the rule of the compound angle
∵
⇒ (1)
∵
⇒ (2)
∵ tan(9x) = equation (2)
- Substitute (2) in (1)
∴ 
- Multiply up and down by (1 - tan(5x)tan(4x))
∴ ![\frac{tan(5x)+tan(4x)-tan(5x)[1-tan(5x)tan(4x)]}{1-tan(5x)tan(4x)+tan(5x)[tan(5x)+tan(4x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%285x%29%2Btan%284x%29-tan%285x%29%5B1-tan%285x%29tan%284x%29%5D%7D%7B1-tan%285x%29tan%284x%29%2Btan%285x%29%5Btan%285x%29%2Btan%284x%29%5D%7D)
- Simplify up and down
∴ 
∴ ![\frac{tan(4x)+tan^{2}(5x)tan(4x)}{[1+tan^{2}(5x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%284x%29%2Btan%5E%7B2%7D%285x%29tan%284x%29%7D%7B%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D)
- Take tan(4x) as a common factor up
∴ ![\frac{tan(4x)[1+tan^{2}(5x)]}{[1+tan^{2}(5x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%284x%29%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D%7B%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D)
- Cancel [1 + tan²(5x)] up and down
∴ The answer is tan(4x)