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\(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
x8 + x4 + 1
= x8 + 2x4 + 1 - x4
= [(x4)2 + 2x4 + 1] - x4
= (x4 + 1)2 - (x2)2
= ( x4 - x2 + 1 ) ( x4 + x2 + 1 )
x8+x+1
=(x8−x2)+(x2+x+1)
=x2(x6−1)+(x2+x+1)
=x2(x2+1)(x3−1)+(x2+x+1)
=x2(x3+1)(x−1)(x2+x+1)+(x2+x+1)
=(x2+x+1)[x2(x3+1)(x−1)+1]
=(x2+x+1)[x2(x4−x3+x−1)+1]
=(x2+x+1)(x6−x5+x3−x2+1)
x6+3x4y2-8x3y3+3x2y4+y6= x6+3x4y2+3x2y4+y6-8x3y3=(x2+y2)3-(2xy)3
= (x2+y2-2xy)[(x2+y2)2+2xy(x2+y2)+(2xy)2]= (x-y)2(x4+6x2y2+y4+2x3y+2xy3)
(x2+y2-5)2-4x2y2-16xy-16=(x2+y2-5)2-(4x2y2+16xy+16)=(x2+y2-5)2-(2xy+4)2
=(x2+y2-5+2xy+4)(x2+y2-5-2xy-4)=(x2+2xy+y2-1)(x2-2xy+y2-9)=[(x+y)2-1][(x-y)2-32]=(x+y-1)(x+y+1)(x-y-3)(x-y+3)
x4+324=x4+36x2+324-36x2=(x2+18)2-(6x)2=(x2+18-6x)(x2+18+6x)
a, \(x^8+x^7+1=x^8-x^2+x^7-x+x^2+x+1=x^2\left(x^6-1\right)+x\left(x^6-1\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x^3-1\right)\left(x^3+1\right)+x\left(x^3-1\right)\left(x^3+1\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)+x\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x^2\left(x-1\right)\left(x^3+1\right)+x\left(x-1\right)\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right)\left[\left(x^3-x^2\right)\left(x^3+1\right)+\left(x^2-x\right)\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right)\left(x^6+x^3-x^5-x^2+x^5+x^2-x^4-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
b, \(x^8+x^4+1=x^8+2x^4+1-x^4=\left(x^4+1\right)^2-x^4=\left(x^4-x^2+1\right)\left(x^4+x^2+1\right)\)
\(=\left(x^4-x^2+1\right)\left(x^4+2x^2+1-x^2\right)=\left(x^4-x^2+1\right)\left[\left(x^2+1\right)-x^2\right]=\left(x^4-x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)
c, \(x^5+x+1=x^5-x^2+x^2+x+1=x^2\left(x^3-1\right)+\left(x^2+x+1\right)=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
\(x^8+x+1\)
\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
1) \(x^6+1\)
\(=x^6+x^4-x^4+x^2-x^2+1\)
\(=\left(x^6-x^4+x^2\right)+\left(x^4-x^2+1\right)\)
\(=x^2\left(x^4-x^2+1\right)+\left(x^4-x^2+1\right)\)
\(=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
2) \(x^6-y^6\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
a, 3x^2 + 13x + 10
= 3x^2 + 3x + 10x + 10
= 3x(x + 1) + 10(x + 1)
= (3x + 10)(x + 1)
b, x^2 - 10x + 21
= x^2 - 3x - 7x + 21
= x(x - 3) - 7(x - 3)
= (x - 7)(x - 3)
c, 6x^2 - 5x + 1
= 6x^2 - 3x - 2x + 1
= 3x(2x - 1) - (2x - 1)
= (3x - 1)(2x - 1)
Bạn đăng 1 lần nhiều bài như vậy làm người khác nản lắm đấy =) đơn giản bài rất dài mà mik cx ko chắc là bản thân mik có đc k hay ko nên phải nản vậy thôi :)
1a)\(3x^2+13x+10=3x^2+3x+10x+10\)
\(3x\left(x+1\right)+10\left(x+1\right)=\left(3x+10\right)\left(x+1\right)\)
b)\(x^2-10x+21=x^2-3x-7x+21\)
\(=x\left(x-3\right)-7\left(x-3\right)=\left(x-7\right)\left(x-3\right)\)
c)\(6x^2-5x+1=6x^2-3x-2x+1\)
\(=3x\left(2x-1\right)-\left(2x-1\right)=\left(3x-1\right)\left(2x-1\right)\)
a) \(x^4+324=\left(x^2-6x+18\right)\left(x^2+6x+18\right)\)
c) \(x^{13}+x^5+1=\left(x^2+x+1\right)\left(x^{11}-x^{10}+x^8-x^7+x^5-x^4+x^3-x+1\right)\)
d) \(x^{11}+x+1=\left(x^2+x+1\right)\left(x^9-x^8+x^6-x^5+x^3-x^2+1\right)\)
e) \(x^8+3x^4+4=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(x^8+3x^4+4\)
\(=x^8+4x^4+4-x^4\)
\(=\left(x^4+2\right)^2-x^4\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)