Так як функція парна то f(x)=f(-x)
тобто f(-18)=f(18)=7
1) xy-5x+3y-15=x(y-5)+3(y-5)=(x+3)(y-5)
2) x^{2}-3x+2x-6=x(x-3)+ 2(x-3)=(x+2)(x-3)
x^{2}-3x+2x-6=x(x+2)-3(x+2)=(x-3)(x+2)
3) xy+4y-3x-12=(x+4)(y-3)
4) x^{3}+7x^{2}-xy-7y=x^{2}(x+7)-y(x+7)=(x^{2}-y)(x+7)
Есть две очень полезные формулы понижения степеней , следующие из формул для косинуса двойного угла (иногда формулы называют "формулы трёх двоечек"):
![sin^2 \alpha =\frac{1-cos2 \alpha }{2}\; \; ,\; \; cos^2 \alpha =\frac{1+cos2 \alpha }{2}](https://tex.z-dn.net/?f=sin%5E2+%5Calpha+%3D%5Cfrac%7B1-cos2+%5Calpha+%7D%7B2%7D%5C%3B+%5C%3B+%2C%5C%3B+%5C%3B+cos%5E2+%5Calpha+%3D%5Cfrac%7B1%2Bcos2+%5Calpha+%7D%7B2%7D)
![sin^2(\frac{\pi }{3}+a)+sin^2(\frac{\pi }{3}-a)+sin^2a=\\\\=\frac{1-cos(\frac{2\pi}{3}+2a)}{2}+\frac{1-cos(\frac{2\pi}{3}-2a)}{2}+\frac{1-cos2a}{2}=\\\\=\frac{1}{2}\cdot (3-cos(\frac{2\pi}{3}+2a)-cos(\frac{2\pi}{3}-2a)-cos2a)=\\\\=[\; cosa+cos \beta =2cos\frac{a+\beta }{2}\cdot cos\frac{a-\beta }{2}\; ]=\\\\=\frac{1}{2}\cdot (3-2\cdot cos\frac{2\pi}{3}\cdot cos2a-cos2a)=\\\\=\frac{1}{2}\cdot (3-2\cdot (-\frac{1}{2})\cdot cos2a-cos2a)=\frac{1}{2}\cdot (3+cos2a-cos2a)=\frac{3}{2}](https://tex.z-dn.net/?f=sin%5E2%28%5Cfrac%7B%5Cpi+%7D%7B3%7D%2Ba%29%2Bsin%5E2%28%5Cfrac%7B%5Cpi+%7D%7B3%7D-a%29%2Bsin%5E2a%3D%5C%5C%5C%5C%3D%5Cfrac%7B1-cos%28%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2a%29%7D%7B2%7D%2B%5Cfrac%7B1-cos%28%5Cfrac%7B2%5Cpi%7D%7B3%7D-2a%29%7D%7B2%7D%2B%5Cfrac%7B1-cos2a%7D%7B2%7D%3D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot+%283-cos%28%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2a%29-cos%28%5Cfrac%7B2%5Cpi%7D%7B3%7D-2a%29-cos2a%29%3D%5C%5C%5C%5C%3D%5B%5C%3B+cosa%2Bcos+%5Cbeta+%3D2cos%5Cfrac%7Ba%2B%5Cbeta+%7D%7B2%7D%5Ccdot+cos%5Cfrac%7Ba-%5Cbeta+%7D%7B2%7D%5C%3B+%5D%3D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot+%283-2%5Ccdot+cos%5Cfrac%7B2%5Cpi%7D%7B3%7D%5Ccdot+cos2a-cos2a%29%3D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot+%283-2%5Ccdot+%28-%5Cfrac%7B1%7D%7B2%7D%29%5Ccdot+cos2a-cos2a%29%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot+%283%2Bcos2a-cos2a%29%3D%5Cfrac%7B3%7D%7B2%7D+++)