Задание 1
(5a-b)²=(5a)²-2*5*a*b+b²=25a²-10ab+b²
(y+6)²=y²+2*6*y+6²=y²+12y+36
(5a-2)(5a+2)=(5a)²-(2)²=25a²-4
(x-0.6)(x+0.6)=x²-(0.6)²=x²-0.36
Задание 2
4a²-25b²=(2a)²-(5b)²=(2a-5b)(2a+5b)
9x²-6xy+y²=(3x)²-2*3*x*y+y²=(3x-y)²=(3x-y)(3x-y)
2ac²-32a³=2a(c²-16a²)=2a(c²-(4a)²)=2a(c-4a)(c+4a)
Задание 3
(a-4)²-(16+2a)=a²-2*4*a+16-16-2a=a²-8a-2a=a²-10a
Задание 4
a²-4b-a+2b=(a-2b)(a+2b)-(a-2b)=(a-2b)(a+2b-1)
9x²+6x+1-4y²=((3x)²+2*3*x+1)-4y²=(3x+1)²-(2y)²=(3x+1-2y)(3x+1-2y)
8c³-27=(2c)³-(3)³=(2c-3)(4c²+6c+9)
X^3-2x^2-9x-18=0
x^3-2x^2-9(x-2)
x^2(x-2)-9(x-2)
(x-2)(x^2-9)=0
(x-2)(x-3)(x+3)=3
x-2=0. x-3=0 x=3. x+3=3 x=3.
x=2
<span>Выборочное среднее:
</span>
![\overline{x}\displaystyle= \frac{\displaystyle\sum_{i}x_in_i}{\displaystyle\sum_in_i} = \frac{7.6\cdot6+8\cdot8+8.4\cdot16+8.8\cdot50+9.2\cdot 30+9.6\cdot15+}{6+8+16+50+30+15+7+5} \\ \\ \frac{10\cdot7+10.4\cdot5}{} = \frac{1226}{137}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cdisplaystyle%3D+%5Cfrac%7B%5Cdisplaystyle%5Csum_%7Bi%7Dx_in_i%7D%7B%5Cdisplaystyle%5Csum_in_i%7D+%3D+%5Cfrac%7B7.6%5Ccdot6%2B8%5Ccdot8%2B8.4%5Ccdot16%2B8.8%5Ccdot50%2B9.2%5Ccdot+30%2B9.6%5Ccdot15%2B%7D%7B6%2B8%2B16%2B50%2B30%2B15%2B7%2B5%7D+%5C%5C+%5C%5C++%5Cfrac%7B10%5Ccdot7%2B10.4%5Ccdot5%7D%7B%7D+%3D+%5Cfrac%7B1226%7D%7B137%7D+)
<span>Выборочная дисперсия равна
</span>
![\widehat{s}^2=\overline{x^2}-\overline{x}^2=\displaystyle \frac{\displaystyle \sum_in_ix_i^2}{\displaystyle \sum_in_i} -\overline{x}^2= \frac{275548}{3425} - \frac{1226^2}{137^2}= \frac{173176}{469225}](https://tex.z-dn.net/?f=%5Cwidehat%7Bs%7D%5E2%3D%5Coverline%7Bx%5E2%7D-%5Coverline%7Bx%7D%5E2%3D%5Cdisplaystyle+%5Cfrac%7B%5Cdisplaystyle+%5Csum_in_ix_i%5E2%7D%7B%5Cdisplaystyle+%5Csum_in_i%7D+-%5Coverline%7Bx%7D%5E2%3D+%5Cfrac%7B275548%7D%7B3425%7D+-+%5Cfrac%7B1226%5E2%7D%7B137%5E2%7D%3D++%5Cfrac%7B173176%7D%7B469225%7D+)
<span>Выборочное среднее квадратическое отклонение равно
</span>
![\widehat{s}= \sqrt{\widehat{s}^2} =\displaystyle \sqrt{\frac{173176}{469225}} = \frac{ \sqrt{173176} }{685}](https://tex.z-dn.net/?f=%5Cwidehat%7Bs%7D%3D+%5Csqrt%7B%5Cwidehat%7Bs%7D%5E2%7D+%3D%5Cdisplaystyle++%5Csqrt%7B%5Cfrac%7B173176%7D%7B469225%7D%7D+%3D+%5Cfrac%7B+%5Csqrt%7B173176%7D+%7D%7B685%7D+)
64а^3+(2-а)^3=(4а+(2-а))(16а^2-4а (2-а)+(2-а)^2)=
=(4а+2-а)(16а^2-8а+4а^2+4-4а+а^2)=
=(3а+2)(21а^2-12а+4)
Х:5-3=х:2
2x-30=5x
2x-5x=30
-3x=30
x=-10