№1
1)
![(-m+5)^{2} =(-m+5)*(-m+5)= m^{2} -5m-5m+25=m^{2}-10m+25](https://tex.z-dn.net/?f=+%28-m%2B5%29%5E%7B2%7D+%3D%28-m%2B5%29%2A%28-m%2B5%29%3D+m%5E%7B2%7D+-5m-5m%2B25%3Dm%5E%7B2%7D-10m%2B25)
2)
![(5a-2b)^{2}= (5a-2b)*(5a-2b)= 25a^{2}-10ab-10ab+4b^{2} =](https://tex.z-dn.net/?f=+%285a-2b%29%5E%7B2%7D%3D+%285a-2b%29%2A%285a-2b%29%3D+25a%5E%7B2%7D-10ab-10ab%2B4b%5E%7B2%7D+%3D+)
![25a^{2}-20ab+4b^{2}](https://tex.z-dn.net/?f=25a%5E%7B2%7D-20ab%2B4b%5E%7B2%7D)
3)
![( p^{3}- q^{3} )^{2} =( p^{3}- q^{3} )*( p^{3}- q^{3} )= p^{6}- p^{3} q^{3}-p^{3} q^{3}+ q^{6}=](https://tex.z-dn.net/?f=+%28+p%5E%7B3%7D-+q%5E%7B3%7D++%29%5E%7B2%7D+%3D%28+p%5E%7B3%7D-+q%5E%7B3%7D++%29%2A%28+p%5E%7B3%7D-+q%5E%7B3%7D++%29%3D+p%5E%7B6%7D-+p%5E%7B3%7D+q%5E%7B3%7D-p%5E%7B3%7D+q%5E%7B3%7D%2B+q%5E%7B6%7D%3D++++)
![p^{6}- 2p^{3} q^{3}+ q^{6}](https://tex.z-dn.net/?f=p%5E%7B6%7D-+2p%5E%7B3%7D+q%5E%7B3%7D%2B+q%5E%7B6%7D)
4)
![( a^{2} -1)^{2} =( a^{2} -1)*( a^{2} -1)= a^{4} -a^{2}-a^{2}+1=a^{4}-2a^{2}+1](https://tex.z-dn.net/?f=+%28+a%5E%7B2%7D+-1%29%5E%7B2%7D+%3D%28+a%5E%7B2%7D+-1%29%2A%28+a%5E%7B2%7D+-1%29%3D+a%5E%7B4%7D+-a%5E%7B2%7D-a%5E%7B2%7D%2B1%3Da%5E%7B4%7D-2a%5E%7B2%7D%2B1)
№2
1) Решим уравнение
![b^{2} +10b+25=0](https://tex.z-dn.net/?f=+b%5E%7B2%7D+%2B10b%2B25%3D0)
a=1 b=10 c=25
Найдем дискриминант уравнения:
![D= b^{2}-4ac= 10^{2}-4*1*25=100-100=0](https://tex.z-dn.net/?f=D%3D+b%5E%7B2%7D-4ac%3D+10%5E%7B2%7D-4%2A1%2A25%3D100-100%3D0++)
Т.к. D=0, то оба корня уравнения будут равны
![x_{1}=x_{2}= \frac{-b+- \sqrt{D} }{2a}= \frac{-10}{2-1}=-5](https://tex.z-dn.net/?f=+x_%7B1%7D%3Dx_%7B2%7D%3D+%5Cfrac%7B-b%2B-+%5Csqrt%7BD%7D+%7D%7B2a%7D%3D+%5Cfrac%7B-10%7D%7B2-1%7D%3D-5+++)
Уравнение имеет два равных корня
![x_{1}=x_{2}=-5](https://tex.z-dn.net/?f=x_%7B1%7D%3Dx_%7B2%7D%3D-5)
, соответственно трехчлен можно разложить по формуле:
![ax^{2}+bx+c=a(x- x_{1} )(x- x_{2})](https://tex.z-dn.net/?f=+ax%5E%7B2%7D%2Bbx%2Bc%3Da%28x-+x_%7B1%7D+%29%28x-+x_%7B2%7D%29+)
![b^{2} +10b+25=(b+5)(b+5)= (b+5)^{2}](https://tex.z-dn.net/?f=b%5E%7B2%7D+%2B10b%2B25%3D%28b%2B5%29%28b%2B5%29%3D+%28b%2B5%29%5E%7B2%7D+)
2) Решим уравнение
![a^{2} -14a+49=0](https://tex.z-dn.net/?f=+a%5E%7B2%7D+-14a%2B49%3D0)
a=1 b=-14 c=49
Найдем дискриминант уравнения:
![D= b^{2}-4ac= (-14)^{2}-4*1*49=196-196=](https://tex.z-dn.net/?f=D%3D+b%5E%7B2%7D-4ac%3D+%28-14%29%5E%7B2%7D-4%2A1%2A49%3D196-196%3D+)
Т.к. D=0, то оба корня уравнения будут равны
![x_{1}=x_{2}= \frac{-b+- \sqrt{D} }{2a}= \frac{14}{2*1}=7](https://tex.z-dn.net/?f=+x_%7B1%7D%3Dx_%7B2%7D%3D+%5Cfrac%7B-b%2B-+%5Csqrt%7BD%7D+%7D%7B2a%7D%3D+%5Cfrac%7B14%7D%7B2%2A1%7D%3D7+)
Уравнение имеет два равных корня
![x_{1}=x_{2}=7](https://tex.z-dn.net/?f=x_%7B1%7D%3Dx_%7B2%7D%3D7)
, соответственно трехчлен можно разложить по формуле:
![ax^{2}+bx+c=a(x- x_{1} )(x- x_{2})](https://tex.z-dn.net/?f=+ax%5E%7B2%7D%2Bbx%2Bc%3Da%28x-+x_%7B1%7D+%29%28x-+x_%7B2%7D%29+)
![a^{2} -14a+49=(a-7})(a-7)=(a-7)^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D+-14a%2B49%3D%28a-7%7D%29%28a-7%29%3D%28a-7%29%5E%7B2%7D)
3) Решим уравнение
![y^{2} +1.8y+0.81=0](https://tex.z-dn.net/?f=+y%5E%7B2%7D+%2B1.8y%2B0.81%3D0)
a=1 b=1.8 c=0.81
Найдем дискриминант уравнения:
![D= b^{2}-4ac= 1.8^{2}-4*1*0.81=3.24-3.24=0](https://tex.z-dn.net/?f=D%3D+b%5E%7B2%7D-4ac%3D+1.8%5E%7B2%7D-4%2A1%2A0.81%3D3.24-3.24%3D0+)
Т.к. D=0, то оба корня уравнения будут равны
![x_{1}=x_{2}= \frac{-b+- \sqrt{D} }{2a}= \frac{-1.8}{2*1}=- \frac{9}{10}=-0.9](https://tex.z-dn.net/?f=x_%7B1%7D%3Dx_%7B2%7D%3D+%5Cfrac%7B-b%2B-+%5Csqrt%7BD%7D+%7D%7B2a%7D%3D+%5Cfrac%7B-1.8%7D%7B2%2A1%7D%3D-+%5Cfrac%7B9%7D%7B10%7D%3D-0.9+)
Уравнение имеет два равных корня
![x_{1}=x_{2}=-0.9](https://tex.z-dn.net/?f=x_%7B1%7D%3Dx_%7B2%7D%3D-0.9)
, соответственно трехчлен можно разложить по формуле:
![ax^{2}+bx+c=a(x- x_{1} )(x- x_{2})](https://tex.z-dn.net/?f=+ax%5E%7B2%7D%2Bbx%2Bc%3Da%28x-+x_%7B1%7D+%29%28x-+x_%7B2%7D%29+)
![y^{2} +1.8y+0.81=(y+0.9)(y+0.9)= (y+0.9)^{2}](https://tex.z-dn.net/?f=y%5E%7B2%7D+%2B1.8y%2B0.81%3D%28y%2B0.9%29%28y%2B0.9%29%3D+%28y%2B0.9%29%5E%7B2%7D+)