3/17 + -8/15 +-3/17 + 8/15 + 2018/2019
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1) 2*17*9+18*540+29*18
= 18*17+18*540+29*18
= 18*(17+540+29)
= 18*586
= 10548
2) 5*{26-[3*(5+2*5)+15]/15}
= 5*{26-[3*(5+10)+15]/15}
= 5*{26-[3*15+15]/15}
= 5*{26-[45+15]/15}
= 5*{26-60/15}
= 5*{26-4}
=5*22
=110
3) (2018*2019+2019*2020)*(45*120-15*360)*(1+5+9+13+17+...+2015+2019)
= (2018*2019+2019*2020)*(15*3*120-15*120*3)*(1+5+9+13+17+...+2015+2019)
= (2018*2019+2019*2020)*0*(1+5+9+13+17+...+2015+2019)
= 0
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Vì A, B < 1
\(A=\frac{15^{16}+1}{15^{17}+1}< \frac{15^{16}+1+14}{15^{17}+1+14}=\frac{15^{16}+15}{15^{17}+15}=\frac{15\left(15^{15}+1\right)}{15\left(15^{16}+1\right)}=\frac{15^{15}+1}{15^{16}+1}\)
b, \(B=\frac{2018^{2018}+1}{2018^{2019}+1}< 1< \frac{2018^{2019}+1}{2018^{2018}+1}=A\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{19}{37}+\left(1-\frac{19}{37}\right)\)
\(=\frac{19}{37}+1-\frac{19}{37}\)
\(=\left(\frac{19}{37}-\frac{19}{37}\right)+1\)
\(=0+1=1\)
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a) x4+x3+2x2+x+1=(x4+x3+x2)+(x2+x+1)=x2(x2+x+1)+(x2+x+1)=(x2+x+1)(x2+1)
b)a3+b3+c3-3abc=a3+3ab(a+b)+b3+c3 -(3ab(a+b)+3abc)=(a+b)3+c3-3ab(a+b+c)
=(a+b+c)((a+b)2-(a+b)c+c2)-3ab(a+b+c)=(a+b+c)(a2+2ab+b2-ac-ab+c2-3ab)=(a+b+c)(a2+b2+c2-ab-ac-bc)
c)Đặt x-y=a;y-z=b;z-x=c
a+b+c=x-y-z+z-x=o
đưa về như bài b
d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung
e)x2(y-z)+y2(z-x)+z2(x-y)=x2(y-z)-y2((y-z)+(x-y))+z2(x-y)
=x2(y-z)-y2(y-z)-y2(x-y)+z2(x-y)=(y-z)(x2-y2)-(x-y)(y2-z2)=(y-z)(x2-2y2+xy+xz+yz)
![](https://rs.olm.vn/images/avt/0.png?1311)
`#3107.101107`
\(-16 \div (-8)+5[3-15\div5+2(-3+4)]\)
`= 2 + 5(3 - 3 - 6 + 8)`
`= 2 + 5*(-6 + 8)`
`= 2 + 5*2`
`= 2(5 + 1)`
`= 2*6 = 12`
____
`15*(-236)+15*235`
`= 15 * (-236 + 235)`
`= 15 * (-1)`
`= -15`
____
`237*(-28)+28*137`
`= 28 * (-237 + 137)`
`= 28 * (-100)`
`= -2800`
____
`(-3)*(-17)+3*(120-17)`
`= 3 * 17 + 3 * (120 - 17)`
`= 3 * (17 + 120 - 17)`
`= 3 * 120`
`= 360`
____
`(-8)*72+8*(-19)-(-8)`
`= 8 * (-72) + 8 * (-19) + 8`
`= 8 * (-72 - 19 + 1)`
`= 8 * (-90)`
`= -720`
a)−16÷(−8)+5[3−15÷5+2(−3+4)]
=2+5(3−3−6+8)
=2+5⋅(−6+8)
=2+5⋅2
=2(5+1)
=2⋅6
=12
b)15⋅(−236)+15⋅235
=15⋅(−236+235)
=15⋅(−1)
=−15
c)237⋅(−28)+28⋅137
=28⋅(−237+137)
=28⋅(−100)
=−2800
d)(−3)⋅(−17)+3⋅(120−17)
=3⋅17+3⋅(120−17)
=3⋅(17+120−17)
=3⋅120
=360
e)(−8)⋅72+8⋅(−19)−(−8)
=8⋅(−72)+8⋅(−19)+8
=8⋅(−72−19+1)
=8⋅(−90)
=−720
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{3}{17}+\dfrac{-8}{15}+\dfrac{-3}{17}+\dfrac{8}{15}+\dfrac{2018}{2019}=\left(\dfrac{3}{17}-\dfrac{3}{17}\right)+\left(\dfrac{8}{15}-\dfrac{8}{15}\right)+\dfrac{2018}{2019}=\dfrac{2018}{2019}\)
\(\dfrac{3}{17}+\dfrac{-8}{15}+\dfrac{-3}{17}+\dfrac{8}{15}+\dfrac{2018}{2019}\)
\(=0+0+\dfrac{2018}{2019}\)
\(=\dfrac{2018}{2019}\)