Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
Bài 1:
a) Ta có: \(x-2y+x^2-4y^2\)
\(=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)\)
\(=\left(x-2y\right)\left(1+x+2y\right)\)
b) Ta có: \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y+2xy\right)\left(x+y-2xy\right)\)
c) Ta có: \(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x^2-1\right)+2x^2\left(x+1\right)\)
\(=x^4\left(x+1\right)\left(x-1\right)+2x^2\left(x+1\right)\)
\(=\left(x+1\right)\left[x^4\left(x-1\right)+2x^2\right]\)
\(=\left(x+1\right)\left(x^5-x^4+2x^2\right)\)
\(=x^2\left(x+1\right)\left(x^3-x^2+2\right)\)
d) Ta có: \(x^3+3x^2+3x+1-8y^3\)
\(=\left(x^3+3x^2+3x+1\right)-\left(2y\right)^3\)
\(=\left(x+1\right)^3-\left(2y\right)^3\)
\(=\left(x+1-2y\right)\left[\left(x+1\right)^2+2y\left(x+1\right)+\left(2y\right)^2\right]\)
\(=\left(x+1-2y\right)\left(x^2+2x+1+2xy+2y+4y^2\right)\)
a) x - 2y + x2 - 4y2
= x - 2y + ( x - 2y).( x+2y)
= (x - 2y).(1+ x + 2y)
b) x2- 4x2y2 + y2 + 2xy
= (x + y)2 - 4x2y2
= (x + y -2xy).(x + y + 2xy)
c) 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+x2-2x2+2)
= x2.(x+1).[x2( x+1) +2 (-x2 +1)]
= x2.(x+1).[x2( x+1) +2 (1+x).(1-x)]
= x2.(x+1)2.(x2 + 2 -2x)
d) x3 + 3x2 + 3x + 1- 8y3
= (x+1)3 - 8y3
= ( x+1 - 2y).[(x+1)2 + (x+1). 2y + 4y2]
= ( x + 1 - 2y).(x2 + 2x + 1 + 2xy + 2y + 4y2)
a/ \(x-2y+x^2-4y^2\)
\(=\left(x-2y\right)+x^2-\left(2y\right)^2\)
\(=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)\)
\(=\left(x-2y\right)\left[1+\left(x+2y\right)\right]\)
\(=\left(x-2y\right)\left(1+x+2y\right)\)
b/ \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)
c/ \(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x^2-1\right)+2x^2\left(x+1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)\)
\(=\left(x+1\right)\left[x^4\left(x-1\right)+2x^2\right]\)
d/ \(x^3+3x^2+3x+1-8y^3\)
\(=\left(x+1\right)^3-\left(2y\right)^3\)
\(=\left(x+1-2y\right)\left[\left(x+1\right)^2+\left(x+1\right)2y+\left(2y\right)^2\right]\)
\(=\left(x+1-2y\right)\left[\left(x^2+2x+1\right)+2xy+2y+4y^2\right]\)
\(=\left(x+1-2y\right)\left(x^2+2x+1+2xy+2y+4y^2\right)\)
a) xy – 3x + 2y – 6
= (xy - 3x) + (2y - 6)
= x(y - 3) + 2(y - 3)
= (y - 3)(x + 2)
b) x2y + 4xy + 4y – y3
= y(x2 + 4x + 4 - y2)
= y[(x2 + 4x + 4) - y2]
= y[(x + 2)2 - y2]
= y(x + 2 + y)(x + 2 - y)
c) x2 + y2 + xz + yz + 2xy
= (x2 + 2xy + y2) + (xz + yz)
= (x + y)2 + z(x + y)
= (x + y)(x + y + z)
d) x3 + 3x2 – 3x – 1
= (x3 - 1) + (3x2 - 3x)
= (x - 1)(x2 + x + z) + 3x(x - 1)
= (x - 1)(x2 + 4x + 1)
a )
\(xy-3x+2y-6\)
\(=\left(xy+2y\right)-3x-6\)
\(=y\left(x+2\right)-3\left(x+2\right)\)
\(=\left(y-3\right)\left(x+2\right)\)
b )
\(x^2y+4xy+4y-y^3\)
\(=y\left(x^2+4x+4-y^2\right)\)
\(=y\left[\left(x+2\right)^2-y^2\right]\)
\(=y\left(x+2-y\right)\left(x+2+y\right)\)
c )
\(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
\(a)\) \(x^2-2x-4y^2-4y\)
\(=\)\(\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
\(=\)\(\left(x-1\right)^2-\left(2y+1\right)^2\)
\(=\)\(\left(x-1-2y-1\right)\left(x-1+2y+1\right)\)
\(=\)\(\left(x-2y-2\right)\left(x+2y\right)\)
\(=\)\(2\left(x-y\right)\left(x+2y\right)\)
Chúc bạn học tốt ~
a) Ta có x2 - 2x - 4y2 - 4y
= x2 - 2x + 1 - 4y2 - 4y - 1
= (x - 1)2 - (4y2 + 4y + 1)
= (x - 1)2 - (2y + 1)2
= (x - 1 - 2y - 1)(x - 1 + 2y + 1)
= (x - 2y - 1)(x + 2y)
a, \((x-2y)+(x+2y)(x-2y)=(x-2y)(1+x+2y)\)
b, \(=(x+y-2xy)(x+y+2xy)\)
c, \(=x^2(x^4-x^2+2x+2)=x^2[x^2(x^2+2x+1)-2x(x^2+2x+1)+2(x^2+2x+1)]=x^2(x^2+2x+1)(x^2-2x+2)=x^2(x+1)^2(x^2+2x+1)\)
d,\(=(x+1)^3-8y^3=(x+1-2y)(x^2+2x+1+2xy+2y+4y^2)\)
Bạn check lại nhé <33