234) разложения квадратного трехчлена на множители:
аx²+bx+c=a(x-x₁)(x-x₂), где x₁ и x₂ - корни уравнения ax²+bx+c=0
решаем квадратное уравнение через дискриминант или по теореме Виета:
![8x^2+8x-16=0 \ \ |:8 \\ x^2+x-2=0 \\ x_1=-2 \\ x_2=1](https://tex.z-dn.net/?f=8x%5E2%2B8x-16%3D0+%5C+%5C+%7C%3A8+%5C%5C+x%5E2%2Bx-2%3D0+%5C%5C+x_1%3D-2+%5C%5C+x_2%3D1)
Таким образом
![8x^2+8x-16=8(x-(-2))(x-1)=8(x+2)(x-1)](https://tex.z-dn.net/?f=8x%5E2%2B8x-16%3D8%28x-%28-2%29%29%28x-1%29%3D8%28x%2B2%29%28x-1%29)
Ответ: (х-1)
240) нельзя разложить на множители только тот квадратный трехчлен, у которого дискриминант меньше нуля (отрицательный)
![2) \ x^2-10x+26=0 \\ \\ D=10^2-4*26=-4\ \textless \ 0](https://tex.z-dn.net/?f=2%29+%5C+x%5E2-10x%2B26%3D0+%5C%5C+%5C%5C+D%3D10%5E2-4%2A26%3D-4%5C+%5Ctextless+%5C+0)
Ответ: 2
1. Преобразуй в многочлен
1) ![(y-4)^{2}=(y-4)(y-4)=y^{2}-4y-4y+16=y^{2}+(-4y-4y)+16=y^{2}-8y+16](https://tex.z-dn.net/?f=%28y-4%29%5E%7B2%7D%3D%28y-4%29%28y-4%29%3Dy%5E%7B2%7D-4y-4y%2B16%3Dy%5E%7B2%7D%2B%28-4y-4y%29%2B16%3Dy%5E%7B2%7D-8y%2B16+)
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2) ![(7x+a)^{2}=(7x+a)(7x+a)=49x^{2}+(7ax+7ax)+a^{2}=49x^{2}+14ax+a^{2}](https://tex.z-dn.net/?f=%287x%2Ba%29%5E%7B2%7D%3D%287x%2Ba%29%287x%2Ba%29%3D49x%5E%7B2%7D%2B%287ax%2B7ax%29%2Ba%5E%7B2%7D%3D49x%5E%7B2%7D%2B14ax%2Ba%5E%7B2%7D)
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3) ![(5c-1)(5c+1)=25c^{2}+(5c-5c)-1=25c^{2}-1](https://tex.z-dn.net/?f=%285c-1%29%285c%2B1%29%3D25c%5E%7B2%7D%2B%285c-5c%29-1%3D25c%5E%7B2%7D-1+)
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4) ![(3a+2b)(3a-2b)=9a^{2}-6ab+6ab-4b^{2}=9a^{2}+(-6ab+6ab)-4b^{2}=9a^{2}-4b^{2}](https://tex.z-dn.net/?f=%283a%2B2b%29%283a-2b%29%3D9a%5E%7B2%7D-6ab%2B6ab-4b%5E%7B2%7D%3D9a%5E%7B2%7D%2B%28-6ab%2B6ab%29-4b%5E%7B2%7D%3D9a%5E%7B2%7D-4b%5E%7B2%7D+)
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2. Упрости выражение
![(a-9)^{2}-(81+2a)=a^{2}-18a+81-81-2a=a^{2}+(-18a-2a)+(81-81)=a^{2}-20a=a(a-20)](https://tex.z-dn.net/?f=%28a-9%29%5E%7B2%7D-%2881%2B2a%29%3Da%5E%7B2%7D-18a%2B81-81-2a%3Da%5E%7B2%7D%2B%28-18a-2a%29%2B%2881-81%29%3Da%5E%7B2%7D-20a%3Da%28a-20%29)
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3. Решите уровнение
![(2-x)^{2}-x(x+1,5)=4](https://tex.z-dn.net/?f=%282-x%29%5E%7B2%7D-x%28x%2B1%2C5%29%3D4)
![4-4x+x^{2}-x^{2}-1,5x=4](https://tex.z-dn.net/?f=4-4x%2Bx%5E%7B2%7D-x%5E%7B2%7D-1%2C5x%3D4)
![4-4x+x^{2}-x^{2}-1,5x-4=0](https://tex.z-dn.net/?f=4-4x%2Bx%5E%7B2%7D-x%5E%7B2%7D-1%2C5x-4%3D0)
![(x^{2}-x^{2})+(-4x-1,5x)+(4-4)=0](https://tex.z-dn.net/?f=%28x%5E%7B2%7D-x%5E%7B2%7D%29%2B%28-4x-1%2C5x%29%2B%284-4%29%3D0)
![-5,5x=0](https://tex.z-dn.net/?f=-5%2C5x%3D0)
![x=0](https://tex.z-dn.net/?f=x%3D0)
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4. Разложите на множители
1) ![x^{2}-49=(x-7)(x+7)](https://tex.z-dn.net/?f=x%5E%7B2%7D-49%3D%28x-7%29%28x%2B7%29)
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2)
![25x^{2}-10xy+y^{2}=25x^{2}+(-5xy-5xy)+y^{2}=(25x^{2}-5xy)+(-5xy+y^{2})=(25x^{2}-5xy)-(5xy-y^{2})=5x(5x-y)-y(5x-y)=(5x-y)(5x-y)=(5x-y)^{2}](https://tex.z-dn.net/?f=25x%5E%7B2%7D-10xy%2By%5E%7B2%7D%3D25x%5E%7B2%7D%2B%28-5xy-5xy%29%2By%5E%7B2%7D%3D%2825x%5E%7B2%7D-5xy%29%2B%28-5xy%2By%5E%7B2%7D%29%3D%2825x%5E%7B2%7D-5xy%29-%285xy-y%5E%7B2%7D%29%3D5x%285x-y%29-y%285x-y%29%3D%285x-y%29%285x-y%29%3D%285x-y%29%5E%7B2%7D)
<span>14а²+ 7ав 7а(2а+в) 7а
----------------- = -------------------- = ----------
</span><span> в²-4а² (в-2а)(в+2а) в-2а</span>
2cos^2x-1-sin4x=0
cos2x-2sin2xcos2x=0
cos2x=0
x=П/4+Пn/2
1-2sin2x=0
sin2x=1/2
x=П/12+Пk
x=5П/12+Пk