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a) Ta có: \(4x^2-6x\)
\(=2x\left(2x-3\right)\)
b) Ta có: \(9x^4y^3+3x^2y^4\)
\(=3x^2y^3\left(3x^2+y\right)\)
c) Ta có: 3(x-y)-5x(y-x)
=3(x-y)+5x(x-y)
=(x-y)(3+5x)
d) Ta có: \(x^3-2x^2+5x\)
\(=x\left(x^2-2x+5\right)\)
e) Ta có: \(5\left(x+3y\right)-15x\left(x+3y\right)\)
\(=\left(x+3y\right)\left(5-15x\right)\)
\(=5\left(x+3y\right)\cdot\left(1-3x\right)\)
f) Ta có: \(2x^2\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^2+4\right)\)
\(=2\left(x+1\right)\left(x^2+2\right)\)
Bài 1:
b: =x^2-10x+x-10
=(x-10)(x+1)
c: \(=2x^2-5x+2x-5=\left(2x-5\right)\left(x+1\right)\)
d: \(=3x^2+5x-3x-5=\left(3x+5\right)\left(x-1\right)\)
e: \(=\left(2x+y\right)^3\)
a) x2 - 7x + 5 = ( x2 - 2 . 7/2 . x + 49 / 4 ) + 5 - 49 / 4
= (x - 7/2)^2 - 29/4
= (x - 7/2)^2 - (√ 29 / 2 )^2
= ( x - ( 7 + √ 29 / 2 )). ( x + ( 7 - √ 29 / 2 ))
a)15x2+20xy2-25xy
= 5x(3x+4y-5)
b) (x+y)2- 25
= (x+y)2- 52
= (x+y+5)(x+y-5)
b) 4x2+8xy+3x-6y
= 4x(x+2y)-3(x+2y)
= (x+2y)(4x-3)
g) 3x2-6xy+3y2
e) 27+27x+9x2+x3
h) 1-4x2
= (1+4x)(1-4x)
c) 1-2y+y2
= y2+y+y-1
= y(y-1)+(y-1)
= (y-1)(y+1)
f) 8-27x3
= 23 - 3x3
= (2-3x)(22+2.3x-3x2)
= (2-3x)(4+6x-9x)
i) x6-x4+2x3-2x
= x(x5-x3+2x2-2)
= x[x3(x2-1)+2(x2-1)]
= x(x2-1)(x3+2)
Bài 5:
a: ĐKXĐ: x<>2; x<>-2
b: \(A=\dfrac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}=\dfrac{x+2}{x-2}\)
c: Để A=2 thì 2x-4=x+2
=>x=6
d)
$x^4+2x^3+2x^2+2x+1$
$=(x^4+2x^3+x^2)+(x^2+2x+1)$
$=(x^2+x)^2+(x+1)^2=x^2(x+1)^2+(x+1)^2$
$=(x+1)^2(x^2+1)$
e)
$x^2y+xy^2+x^2z+y^2z+2xyz$
$=xy(x+y)+z(x^2+y^2)+2xyz$
$=xy(x+y)+z(x^2+y^2+2xy)$
$=xy(x+y)+z(x+y)^2=(x+y)(xy+zx+zy)$
f)
$x^5+x^4+x^3+x^2+x+1$
$=(x^5+x^4)+(x^3+x^2)+(x+1)=x^4(x+1)+x^2(x+1)+(x+1)$
$=(x+1)(x^4+x^2+1)$
$=(x+1)[(x^4+2x^2+1)-x^2]$
$=(x+1)[(x^2+1)^2-x^2]=(x+1)(x^2+1-x)(x^2+1+x)$
a)
$x^4-2x^3+2x-1=(x^4-2x^3+x^2)-(x^2-2x+1)$
$=(x^2-x)^2-(x-1)^2$
$=x^2(x-1)^2-(x-1)^2=(x-1)^2(x^2-1)=(x-1)^2(x-1)(x+1)$
$=(x-1)^3(x+1)$
b)
$a^6-a^4+2a^3+2a^2$
$=a^4(a^2-1)+2a^2(a+1)$
$=a^4(a-1)(a+1)+2a^2(a+1)$
$=(a+1)[a^4(a-1)+2a^2]$
$=a^2(a+1)[a^2(a-1)+2]$
$=a^2(a+1)(a^3-a^2+2)=a^2(a+1)[a^2(a+1)-2(a^2-1)]$
$=a^2(a+1)[a^2(a+1)-2(a-1)(a+1)]$
$=a^2(a+1)(a+1)(a^2-2a+2)=a^2(a+1)^2(a^2-2a+2)$
c)
$x^4+x^3+2x^2+x+1$
$=(x^4+2x^2+1)+(x^3+x)$
$=(x^2+1)^2+x(x^2+1)=(x^2+1)(x^2+1+x)$
a) \(5\left(x+4\right)-2x\left(4+x\right)\)
\(=\left(x+4\right)\left(5-2x\right)\)
b) \(\left(x-2017\right)x-5\left(2017-x\right)\)
\(=\left(x-2017\right)x+5\left(x-2017\right)\)
\(=\left(x-2017\right)\left(x+5\right)\)
c) \(\left(x+1\right)^2-\left(x+1\right)\)
\(=\left(x+1\right)\left(x+1-1\right)\)
= \(x\left(x+1\right)\)
d) \(9x^2\left(y-1\right)-18x\left(1-y\right)\)
\(=9x^2\left(y-1\right)+18x\left(y-1\right)\)
\(=\left(y-1\right)\left(9x^2+18x\right)\)
\(=9x\left(y-1\right)\left(x+2\right)\)
e) \(100x^2y-25xy^2-5xy\)
\(=5xy\left(20x-5y-1\right)\)
f) \(\left(n+1\right)n-\left(n+1\right)3\)
\(=\left(n+1\right)\left(n-3\right)\)