а) 5a(2 - a) + 6a(a - 7) = 10а - 5а² + 6а² - 42а = а² - 32а;
b) (b - 3)(b - 4)(b + 4)² = (b² - 4b - 3b + 12)(b² + 8b + 16) = (b² - 7b + 12)(b² + 8b + 16) = b⁴ + 8b³ + 16b² - 7b³ - 56b² - 112b + 12b² + 96b + 192 = b⁴ + b³ - 28b² - 16b + 192;
c) 20х + 5(х - 2)² = 20х + 5(х² - 4х + 4) = 20х + 5х² - 20х + 20 = 5х² + 20.
Если y(-x) = y(x) -- функция четная,
если y(-x) = -y(x) -- функция нечетная.
![1) \: \: y( - x) = 3cos( - x)sin( - x) - tg( - x) = 3cosx \times ( - sinx) - ( - tgx) = - 3cosxsinx + tgx = - (3cosxsinx - tgx) = - y(x)](https://tex.z-dn.net/?f=1%29+%5C%3A+%5C%3A+y%28+-+x%29+%3D+3cos%28+-+x%29sin%28+-+x%29+-+tg%28+-+x%29+%3D+3cosx+%5Ctimes+%28+-+sinx%29+-+%28+-+tgx%29+%3D+-+3cosxsinx+%2B+tgx+%3D+-+%283cosxsinx+-+tgx%29+%3D+-+y%28x%29)
=> функция нечетная.
![2) \: \: y( - x) = {tg}^{2} ( - x) - 5cos( -x) \div sin( - x) = {tg}^{2} x - 5cosx \div ( - sinx) = {tg}^{2} x + 5cosx \div sinx](https://tex.z-dn.net/?f=2%29+%5C%3A+%5C%3A+y%28+-+x%29+%3D+%7Btg%7D%5E%7B2%7D+%28+-+x%29+-+5cos%28+-x%29+%5Cdiv+sin%28+-+x%29+%3D+%7Btg%7D%5E%7B2%7D+x+-+5cosx+%5Cdiv+%28+-+sinx%29+%3D+%7Btg%7D%5E%7B2%7D+x+%2B+5cosx+%5Cdiv+sinx)
=> функция ни четная, ни нечетная.
![3) \: \: y( - x) = - x \times ctg( - x) - 2cos( - x) = - x \times ( - ctgx) - 2cosx = xctgx - 2cosx = y(x)](https://tex.z-dn.net/?f=3%29+%5C%3A+%5C%3A+y%28+-+x%29+%3D+-+x+%5Ctimes+ctg%28+-+x%29+-+2cos%28+-+x%29+%3D+-+x+%5Ctimes+%28+-+ctgx%29+-+2cosx+%3D+xctgx+-+2cosx+%3D+y%28x%29)
=> функция четная.
![4) \: \: y( - x) = {sin}^{2}(-x) - cos(-x) + {(-x)}^{3} tg(-x) = {sin}^{2}x - cosx - ({x}^{3}) \times (-tgx) = {sin}^{2} - cosx + {x}^{3}tgx = y(x)](https://tex.z-dn.net/?f=+4%29+%5C%3A+%5C%3A+y%28+-+x%29+%3D+%7Bsin%7D%5E%7B2%7D%28-x%29+-+cos%28-x%29+%2B+%7B%28-x%29%7D%5E%7B3%7D+tg%28-x%29+%3D++%7Bsin%7D%5E%7B2%7Dx+-+cosx+-+%28%7Bx%7D%5E%7B3%7D%29+%5Ctimes+%28-tgx%29+%3D+%7Bsin%7D%5E%7B2%7D+-+cosx+%2B+%7Bx%7D%5E%7B3%7Dtgx+%3D+y%28x%29+)
=> функция четная.
![5) \: \: y( -x) = 2sin(-x) - cos(-x) = -2sinx - cosx](https://tex.z-dn.net/?f=+5%29+%5C%3A+%5C%3A+y%28+-x%29+%3D+2sin%28-x%29+-+cos%28-x%29+%3D+-2sinx+-+cosx+)
=> функция ни четная, ни нечетная.
A15=a1+d*14=-3+5*14=70-3=67
a14=a15-a=67-5=62
s15=((a1+a15)/2)*15=((-3+67)/2)*15=(64/2)*15=32*15=480
s14=((a1+a14)/2)*14=((=3+62)/2)*14)=(59/2)*14=59*7=413
s15-s14=480-413=67