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đề đáng lẽ phải là: \(x^7+x^2+1\)
\(x^7+x^2+1=\left(x^7-x\right)+\left(x^2+x+1\right)\)
\(=x\left(x^6-1\right)+\left(x^2+x+1\right)\)
\(=x\left(x^3-1\right)\left(x^3+1\right)+\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)+\left(x^2+x+1\right)\)
\(=\left[x\left(x-1\right)\left(x+3\right)+1\right]\left(x^2+x+1\right)\)
\(=\left[\left(x^2-x\right)\left(x^3+1\right)+1\right]\left(x^2+x+1\right)\)
\(=\left(x^5-x^4-x^2-x+1\right)\left(x^2+x+1\right)\)
\(\dfrac{xy}{2}-x+\dfrac{x^2}{4}=x\left(\dfrac{y}{2}-1+\dfrac{x}{4}\right)\)
A=x14+x7+1
=(x14+x13+x12)-(x13+x12+x11)+(x11+x10+x9)-(x10+x9+x8)+(x8+x7+x6)-(x6+x5+x4)+(x5+x4+x3)-(x3+x2+x)+(x2+x+1)
Đặt B=x2+x+1
=>A=x12B-x11B+x9B-x8B+x6B-x4B+x3B-xB+B
=>A=B(x12-x11+x9-x8+x6-x4+x3-x+1)
Thay B=x2+x+1 vào A là xong
Bài khó quá
4x⁴+4x-3= (2x)²+2(2x)+1-4
=(2x+1)²-2²=(2x+1-2)(2x+1+2)
=(2x-1)(2x+3)
1/(x+2)2 -(3x-1)2=(x+2+3x-1)(x+2-3x+1)=4x(-2x+3)=-8x2+12x
2/(x4+x2)(-2x3-2x)=x2(x2+1)-2x(x2+1)=(x2+1)(x2-2x)
1, = 6(x^2 .y -z^2 +10x+25 )
2, = x^2 -2x-9x+18
= x(x-2)-9(x-2)
= (x-9)(x-2)
x^8 + x + 1 = (x^8 + x^7 + x^6) - ( x^7 + x^6 + x^5) + (x^5 + x^4 + x^3) -(x^4 + x^3 + x^2) + (x^2+x+1)
= (x^2+x+1)(x^6 - x^5 + x^3 - x^2 +1)
Ta có \(x^8+x+1=x^8-x^2+x^2+x+1\)
\(=x^2\left(x^6-1\right)+x^2+x+1\)
\(=x^2\left(x^3-1\right)\left(x^3+1\right)+x^2+x+1\)
\(=\left(x^3-1\right)\left(x^5+x^2\right)+x^2+x+1\)
\(=\left(x-1\right)\left(x^2+x+1\right)\left(x^5+x^2\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\text{[}\left(x-1\right)\left(x^5+x^2\right)+1\text{]}\text{ }\)
\(=\left(x^2+x+1\right)\left(x^6+x^3-x^5-x^2+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
Vậy \(x^8+x+1=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
\(64-x^2-y^2+2xy=64-\left(x^2-2xy+y^2\right)\)
\(=8^2-\left(x-y\right)^2=\left(8-x+y\right)\left(8+x-y\right)\)
em chiu a. chang hieu gi hihi
1)(5-x2).(x4+5x2+25)
2)15.(x-1)-(3x-1)
3)(x2-2)2
4)36x2.(y-1)
5)(7-y).(z-x)
6)(x+3).(x+5)
7)(x-10).(x+2)
8)(x+5).(3y+1)
9)(-(y-x-3)).(y-x+3)
10)(11-x).(y+x)
11)(y-x+3)).(y+x-3)
12)(-(y+2x-5)).(y+2x+5)
13)4.(tz+y2+(-x).y-t2
14)(8-x).(y-x)