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CM
31 tháng 1 2018
a) x6 – x4 + 2x3 + 2x2
= x2(x4 – x2 + 2x + 2)
= x2[x2(x2 – 1) + 2(x + 1)]
= x2. [x2.(x -1).(x + 1) + 2(x+ 1)]
= x2 (x+ 1).[x2(x- 1)+ 2]
= x2(x + 1)(x3 – x2 + 2)
= x2(x + 1)[(x3 + 1) – (x2 – 1)]
= x2(x + 1).[(x + 1).(x2 – x + 1) - (x - 1).(x + 1)]
= x2(x + 1)(x + 1)( x2 – x + 1 – x + 1)
= x2(x + 1)2(x2 – 2x + 2).
b) 4x4 + y4 = 4x4 + 4x2y2 + y4 - 4x2y2
= (2x2 + y2)2 - (2xy)2
= (2x2 + y2 + 2xy)(2x2 + y2 - 2xy)
CM
25 tháng 12 2018
a) (x - y)(x + y + 3). b) (x + y - 2xy)(2 + y + 2xy).
c) x 2 (x + l)( x 3 - x 2 + 2). d) (x – 1 - y)[ ( x - 1 ) 2 + ( x - 1 ) y + y 2 ].
AH
Akai Haruma
Giáo viên
25 tháng 10 2021
a.
$x^2-y^2-2x+2y=(x^2-y^2)-(2x-2y)=(x-y)(x+y)-2(x-y)=(x-y)(x+y-2)$
b.
$x^2(x-1)+16(1-x)=x^2(x-1)-16(x-1)=(x-1)(x^2-16)=(x-1)(x-4)(x+4)$
c.
$x^2+4x-y^2+4=(x^2+4x+4)-y^2=(x+2)^2-y^2=(x+2-y)(x+2+y)$
d.
$x^3-3x^2-3x+1=(x^3+1)-(3x^2+3x)=(x+1)(x^2-x+1)-3x(x+1)$
$=(x+1)(x^2-4x+1)$
AH
Akai Haruma
Giáo viên
25 tháng 10 2021
e.
$x^4+4y^4=(x^2)^2+(2y^2)^2+2.x^2.2y^2-4x^2y^2$
$=(x^2+2y^2)^2-(2xy)^2=(x^2+2y^2-2xy)(x^2+2y^2+2xy)$
f.
$x^4-13x^2+36=(x^4-4x^2)-(9x^2-36)$
$=x^2(x^2-4)-9(x^2-4)=(x^2-9)(x^2-4)=(x-3)(x+3)(x-2)(x+2)$
g.
$(x^2+x)^2+4x^2+4x-12=(x^2+x)^2+4(x^2+x)-12$
$=(x^2+x)^2-2(x^2+x)+6(x^2+x)-12$
$=(x^2+x)(x^2+x-2)+6(x^2+x-2)=(x^2+x-2)(x^2+x+6)$
$=[x(x-1)+2(x-1)](x^2+x+6)=(x-1)(x+2)(x^2+x+6)$
h.
$x^6+2x^5+x^4-2x^3-2x^2+1$
$=(x^6+2x^5+x^4)-(2x^3+2x^2)+1$
$=(x^3+x^2)^2-2(x^3+x^2)+1=(x^3+x^2-1)^2$
D
3
DN
2
NV
Nguyễn Việt Lâm
Giáo viên
1 tháng 9 2021
\(=\left(x^6+2x^5+x^4\right)-2\left(x^5+2x^4+x^3\right)+2\left(x^4+2x^3+x^2\right)\)
\(=x^2\left(x^2+x\right)^2-2x\left(x^2+x\right)^2+2\left(x^2+x\right)^2\)
\(=\left(x^2+x\right)^2\left(x^2-2x+2\right)\)
\(=x^2\left(x+1\right)^2\left(x^2-2x+2\right)\)
6 tháng 6 2017
1) \(x^2-7x+6=x^3+1-7x-7=\left(x^3+1\right)-7\left(x+1\right)=\left(x+1\right)\left(x^2-x-6\right)\)
2) \(x^3-9x^2+6x+16\)
\(\left(x^3+1\right)-\left[\left(9x^2-6x+1\right)-16\right]\)
\(=\left(x^3+1\right)-\left[\left(3x-1\right)^2-16\right]=\left(x^3+1\right)-\left(3x-1+4\right)\left(3x-1-4\right)\)\(=\left(x^3+1\right)-3\left(3x-5\right)\left(x+1\right)\)\(=\left(x+1\right)\left[x^2-x+1-9x+15\right]=\left(x+1\right)\left(x^2-10x+16\right)\)
\(=\left(x+1\right)\left[x\left(x-2\right)-8\left(x-2\right)\right]\)\(\left(x+1\right)\left(x-2\right)\left(x-8\right)\)
3) \(x^3-6x^2-x+30\)
\(=x^3-5x^2-x^2+5x-6x+30\)
\(=x^2\left(x-5\right)-x\left(x-5\right)-6\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2-x-1\right)\)
4) \(2x^3-x^2+5x+3=\left(2x^3+x^2\right)-\left(2x^2+x\right)+\left(6x+3\right)\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
5) \(27x^3-27x^2+18x-4=\left(27x^3-1\right)-\left(27x^2-18x+3\right)\)
\(=\left(3x-1\right)\left(9x^2+3x+1\right)-3\left(9x^2-6x+1\right)\)
\(=\left(3x-1\right)\left(9x^2+3x+1\right)-3\left(3x-1\right)^2\)
\(=\left(3x-1\right)\left(9x^2+3x+1-9x+3\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)
gửi phần này trước còn lại làm sau !!! tk mk nka !!!
28 tháng 6 2021
6) Ta có: \(x^2+2xy+y^2-x-y-12\)
\(=\left(x+y\right)^2-\left(x+y\right)-12\)
\(=\left(x+y-4\right)\left(x+y+3\right)\)
7) Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
8) Ta có: \(4x^4-32x^2+1\)
\(=4x^4+12x^3+2x^2-12x^3-36x^2-6x+2x^2+6x+1\)
\(=2x^2\left(2x^2+6x+1\right)-6x\left(2x^2+6x+1\right)+\left(2x^2+6x+1\right)\)
\(=\left(2x^2+6x+1\right)\left(2x^2-6x+1\right)\)
9) Ta có: \(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)
\(=3\left[x^4+2x^2+1-x^2\right]-\left(x^2+x+1\right)^2\)
\(=3\left(x^2-x+1\right)\left(x^2+x+1\right)-\left(x^2+x+1\right)^2\)
\(=\left(x^2+x+1\right)\left(3x^2-3x+3-x^2-x-1\right)\)
\(=\left(x^2+x+1\right)\left(2x^2-4x+2\right)\)
\(=2\left(x-1\right)^2\cdot\left(x^2+x+1\right)\)
KV
17 tháng 7 2023
a) 6x² + 7xy + 2y²
= 6x² + 4xy + 3xy + 2y²
= (6x² + 4xy) + (3xy + 2y²)
= 2x(3x + 2y) + y(3x + 2y)
= (3x + 2y)(2x + y)
b) x² - y² + 10x - 6y + 16
= x² + 10x + 25 - y² - 6y - 9
= (x² + 10x + 25) - (y² + 6y + 9)
= (x + 5)² - (y + 3)²
= (x + 5 - y - 3)(x + 5 + y + 3)
= (x - y + 2)(x + y + 8)
c) 4x⁴ + y⁴
= 4x⁴ + 4x²y² + y⁴ - 4x²y²
= (2x² + y²)² - (2xy)²
= (2x² + y² - 2xy)(2x² + y² + 2xy)
9 tháng 12 2021
a) 2x. (x2 – 7x -3)
= 2x3- 14x2- 6x
b) ( -2x3 + y2 -7xy). 4xy2
= -8x4y2+ 4xy4- 28x2y3
c)(-5x3).(2x2+3x-5)
= -10x5-15x4+25x3
d) (2x2 - xy+ y2).(-3x3)
=-6x5+ 3x4y -3x3y2
e)(x2 -2x+3). (x-4)
=x3-2x2+3x -4x2+8x-12
=x3-6x2+11x-12
f) ( 2x3 -3x -1). (5x+2)
=10x4-15x2-5x +4x3-6x-2
=10x4+4x3-15x2-11x-2
blablablablablu
blublublu
chúc bn hok tốt
ĐỀ SAI À???