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[Thái Sơn Long]

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a) 4x^2-4x-9y^2+1
b)x^2-10x+25
c)-x^2+1/4
d)x^3+x^2y-x^2z-xyz
e)x^2+2xy^2-xz-yz+y^2
f)x^3+3x^2+3x-8y^3+1
g)4x^2+8x-5
k)3x^2-5x+1
h)(x+1).(x+2).(x+3).(x+4)-24
m)4x^2y^2-(x^2+y^2-z^2)^2
n)x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)
i)2x^2-x+y-2y^2

 

[damdamty]

b) x^2-10x+25
= x^2-5x-5x+25-25+25
= x(x-5)-5(x-5)= (x-5)^2
p/s: hoa mắt quá nên chỉ lm 1 câu thui ~

 

[Blue Plus]

a) 4x^2-4x-9y^2+1
b)x^2-10x+25
c)-x^2+1/4
d)x^3+x^2y-x^2z-xyz
e)x^2+2xy^2-xz-yz+y^2
f)x^3+3x^2+3x-8y^3+1
g)4x^2+8x-5
k)3x^2-5x+1
h)(x+1).(x+2).(x+3).(x+4)-24
m)4x^2y^2-(x^2+y^2-z^2)^2
n)x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)
i)2x^2-x+y-2y^2

a,
[tex]\dpi{100} 4x^2-4x-9y^2+1\\=4x^2-4x+1-9y^2\\=(2x-1)^2-(3y)^2\\=(2x-1+3y)(2x-1-3y)[/tex]
b,
[tex]\dpi{100} x^2-10x+25=(x-5)^2[/tex]
c,
[tex]\dpi{100} -x^2+\frac{1}{4}\\=\frac{1}{4}-x^2\\=(\frac{1}{2}+x)(\frac{1}{2}-x)[/tex]
d,
[tex]\dpi{100} x^3+x^2y-x^2z-xyz\\=x^2(x+y)-xz(x+y)\\=(x^2-xz)(x+y)\\=x(x-z)(x+y)[/tex]
e,
Đề phải thế này chớ [tex]\dpi{100} x^2+2xy-xz-yz+y^2[/tex]
f,
[tex]\dpi{100} x^3+3x^2+3x-8y^3+1\\=x^3+3x^2+3x+1-8y^3\\=(x+1)^3-(2y)^3\\=(x+1-2y)[(x+1)^2+2y(x+1)+4y^2]\\=(x+1-2y)(x^2+2x+1+2xy+2y+4y^2)[/tex]
g,
[tex]\dpi{100} 4x^2+8x-5\\=4x^2-2x+10x-5\\=2x(2x-1)+5(2x-1)\\=(2x-1)(2x+5)[/tex]
h,
[tex]\dpi{100} (x+1)(x+2)(x+3)(x+4)-24\\=(x^2+x+2x+2)(x^2+3x+4x+12)\\=(x^2+3x+2)(x^2+7x+12)-24\\=x^4+7x^3+12x^2+3x^3+21x^2+36x+2x^2+14x+24-24\\=x^4+10x^3+35x^2+50x\\=x(x^3+10x^2+35x+50)\\=x(x^3+5x^2+5x^2+25x+10x+50)\\=x[x^2(x+5)+5x(x+5)+10(x+5)]\\=x(x+5)(x^2+5x+10)[/tex]
i,
[tex]\dpi{100} 2x^2-x+y-2y^2\\=2x^2-2y^2-x+y\\=2(x^2-y^2)-(x-y)\\=2(x+y)(x-y)-(x-y)\\=(x-y)[2(x+y)-1]=(x+y)(2x+2y-1)[/tex]

 

[shirona]

a) 4x^2-4x-9y^2= (4x^2-4x+1) -9x^2= (2x-1)^2 - (3x)^2= (2x-1-3x). (2x-1+3x)= (-x-1).(5x-1)
b) (x-5)^2
c)-x^2+1/4= - [x^2-(1/2)^2]= - (x-1/2).(x+1/2)
d)x^3+x^2y-x^2z-xyz= (x^3+x^2y)-(x^2+xyz)=x^2. (x+y)-xz.(x+y)= x. (x-z).(x+y)
g)4x^2+8x-5= (4x^2+8x+4)-4-5= (2x+2)^2 -9= (2x+2)^2-3^2= (2x+2-3).(2x+2+3)= (2x-1).(2x+5)
P/S phần còn lại đnag làm.

 

[Thái Sơn Long]

a,
[tex]\dpi{100} 4x^2-4x-9y^2+1\\=4x^2-4x+1-9y^2\\=(2x-1)^2-(3y)^2\\=(2x-1+3y)(2x-1-3y)[/tex]
b,
[tex]\dpi{100} x^2-10x+25=(x-5)^2[/tex]
c,
[tex]\dpi{100} -x^2+\frac{1}{4}\\=\frac{1}{4}-x^2\\=(\frac{1}{2}+x)(\frac{1}{2}-x)[/tex]
d,
[tex]\dpi{100} x^3+x^2y-x^2z-xyz\\=x^2(x+y)-xz(x+y)\\=(x^2-xz)(x+y)\\=x(x-z)(x+y)[/tex]
e,
Đề phải thế này chớ [tex]\dpi{100} x^2+2xy-xz-yz+y^2[/tex]
f,
[tex]\dpi{100} x^3+3x^2+3x-8y^3+1\\=x^3+3x^2+3x+1-8y^3\\=(x+1)^3-(2y)^3\\=(x+1-2y)[(x+1)^2+2y(x+1)+4y^2]\\=(x+1-2y)(x^2+2x+1+2xy+2y+4y^2)[/tex]
g,
[tex]\dpi{100} 4x^2+8x-5\\=4x^2-2x+10x-5\\=2x(2x-1)+5(2x-1)\\=(2x-1)(2x+5)[/tex]
h,
[tex]\dpi{100} (x+1)(x+2)(x+3)(x+4)-24\\=(x^2+x+2x+2)(x^2+3x+4x+12)\\=(x^2+3x+2)(x^2+7x+12)-24\\=x^4+7x^3+12x^2+3x^3+21x^2+36x+2x^2+14x+24-24\\=x^4+10x^3+35x^2+50x\\=x(x^3+10x^2+35x+50)\\=x(x^3+5x^2+5x^2+25x+10x+50)\\=x[x^2(x+5)+5x(x+5)+10(x+5)]\\=x(x+5)(x^2+5x+10)[/tex]
i,
[tex]\dpi{100} 2x^2-x+y-2y^2\\=2x^2-2y^2-x+y\\=2(x^2-y^2)-(x-y)\\=2(x+y)(x-y)-(x-y)\\=(x-y)[2(x+y)-1]=(x+y)(2x+2y-1)[/tex]
k, Sai đề

câu e đề vậy đó bạn mk nhầm

 

[Blue Plus]

câu e đề vậy đó bạn mk nhầm

e,
[tex]\dpi{100} x^2+2xy-xz-yz+y^2\\=x^2+2xy+y^2-(xz+yz)\\=(x+y)^2-z(x+y)\\=(x+y-z)(x+y)[/tex]
còn kmn nhường cj @Nữ Thần Mặt Trăng, e bí

 

[trunghieule2807]

k)3x^2-5x+1

[tex]3x^{2}-5x+1=0[/tex]
[tex]\Delta =5^{2}-4.3=13[/tex]
Phương trình có hai nghiệm phân biệt là:
[tex]x_{1}=\frac{5-\sqrt{13}}{6};x_{2}=\frac{5+\sqrt{13}}{6}[/tex]
[tex]\Rightarrow 3x^{2}-5x+1=\frac{(6x-5-\sqrt{13})(6x-5+\sqrt{13})}{12}[/tex]

 

[Nữ Thần Mặt Trăng]

k)3x^2-5x+1
m)4x^2y^2-(x^2+y^2-z^2)^2
n)x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)

$k)3x^2-5x+1$
$=3(x^2-\dfrac 53x+\dfrac{25}{36}-\dfrac{13}{36})$
$=3\left [ (x-\dfrac 56)^2-\dfrac{13}{36} \right ]$
$=3(x-\dfrac 56-\dfrac{\sqrt{13}}6)(x-\dfrac 56+\dfrac{\sqrt{13}}6)$
$=3(x-\dfrac{5+\sqrt{13}}6)(x-\dfrac{5-\sqrt{13}}6)$
$m)4x^2y^2-(x^2+y^2-z^2)^2$
$=(2xy+x^2+y^2-z^2)(2xy-x^2-y^2+z^2)$
$=[(x+y)^2-z^2][z^2-(x-y)^2]$
$=(x+y+z)(x+y-z)(z+x-y)(z-x+y)$
$n)x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)$
$=xy^2-xz^2+yz^2-x^2y+z(x+y)(x-y)$
$=-(x^2y-xy^2)-(xz^2-yz^2)+(xz+yz)(x-y)$
$=-xy(x-y)-z^2(x-y)+(xz+yz)(x-y)$
$=(x-y)(-xy-z^2+xz+yz)$
$=(x-y)[-x(y-z)+z(y-z)]$
$=(x-y)(y-z)(z-x)$

 

[Nguyễn Kim Ngọc]

a) 4x^2-4x-9y^2+1
b)x^2-10x+25
c)-x^2+1/4
d)x^3+x^2y-x^2z-xyz
e)x^2+2xy^2-xz-yz+y^2
f)x^3+3x^2+3x-8y^3+1
g)4x^2+8x-5
k)3x^2-5x+1
h)(x+1).(x+2).(x+3).(x+4)-24
m)4x^2y^2-(x^2+y^2-z^2)^2
n)x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)
i)2x^2-x+y-2y^2

[tex]n)x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)[/tex]
[tex]=x(y^2-z^2)-y[(y^2-z^2)+(x^2-y^2)]+z(x^2-y^2)[/tex]
[tex]=x(y^2-z^2)-y(y^2-z^2)-y(x^2-y^2)+z(x^2-y^2)[/tex]
[tex]=(x-y)(y-z)(y+z)-(y-z)(x-y)(x+y)[/tex]
[tex]=(x-y)(y-z)(z-x)[/tex]