![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,=\left(x-2\right)^2-y^2=\left(x-y-2\right)\left(x+y-2\right)\\ b,=4x^2\left(x^2+2x+1\right)=4x^2\left(x+1\right)^2\\ c,=xy^2\left(x^2-2xy+y^2\right)=xy^2\left(x-y\right)^2\\ d,=\left(x-y\right)\left(x+y\right)-7\left(x-y\right)=\left(x-y\right)\left(x+y-7\right)\\ e,=\left(5x-2y\right)\left(5x+2y\right)\\ f,=x^2+3x+4x+12=\left(x+3\right)\left(x+4\right)\\ i,=x^2+2x-7x-14=\left(x+2\right)\left(x-7\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
câu a) x^5 +x+1=x^5 -x^2 +x^2 +x+1=x^2(x^3-1) +x^2 +x+1=x^2(x-1)(x^2+x+1) +x^2 +x+1=(x^2+x+1)(x^3-x^2 +1)
![](https://rs.olm.vn/images/avt/0.png?1311)
b) \(25-x^2+14xy-49y^2\)
\(=25-\left(x^2-14xy+49y^2\right)\)
\(=25-\left[x^2-2\cdot7y\cdot x+\left(7y\right)^2\right]\)
\(=25-\left(x-7y\right)^2\)
\(=5^2-\left(x-7y\right)^2\)
\(=\left[5-\left(x-7y\right)\right]\left[5+\left(x-7y\right)\right]\)
\(=\left(5-x+7y\right)\left(5+x-7y\right)\)
c) \(x^5+x^4+1\)
\(=x^5+x^4+1+x^3-x^3\)
\(=\left(x^5+x^4+x^3\right)+\left(1-x^3\right)\)
\(=x^3\left(x^2+x+1\right)+\left(1-x\right)\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x^3+\left(1-x\right)\right]\)
\(=\left(x^2+x+1\right)\left(x^3+1-x\right)\)
b: 25-x^2+14xy-49y^2
=25-(x-7y)^2
=(5-x+7y)(5+x-7y)
c: =x^5+x^4+x^3+1-x^3
=x^3(x^2+x+1)+(1-x)(x^2+x+1)
=(x^2+x+1)(x^3+1-x)
![](https://rs.olm.vn/images/avt/0.png?1311)
a. $6x^2-11x=x(6x-11)$
b. $x^7+x^5+1=(x^7-x)+(x^5-x^2)+x+x^2+1$
$=x(x^6-1)+x^2(x^3-1)+(x^2+x+1)$
$=x(x^3-1)(x^3+1)+x^2(x^3-1)+(x^2+x+1)$
$=(x^3-1)(x^4+x+x^2)+(x^2+x+1)$
$=(x-1)(x^2+x+1)(x^4+x^2+x)+(x^2+x+1)$
$=(x^2+x+1)[(x-1)(x^4+x^2+x)+1]$
$=(x^2+x+1)(x^5-x^4+x^3-x+1)$
c.
$x^8+x^4+1=(x^4)^2+2.x^4+1-x^4$
$=(x^4+1)^2-(x^2)^2$
$=(x^4+1-x^2)(x^4+1+x^2)$
$=(x^4+1-x^2)(x^4+2x^2+1-x^2)$
$=(x^4-x^2+1)[(x^2+1)^2-x^2]$
$=(x^4-x^2+1)(x^2+1-x)(x^2+1+x)$
d.
$x^3-5x+8-4=x^3-5x+4$
$=x^3-x^2+x^2-x-(4x-4)$
$=x^2(x-1)+x(x-1)-4(x-1)=(x-1)(x^2+x-4)$
e.
$x^5+x^4+1=(x^5-x^2)+(x^4-x)+x^2+x+1$
$=x^2(x^3-1)+x(x^3-1)+x^2+x+1$
$=(x^3-1)(x^2+x)+(x^2+x+1)$
$=(x-1)(x^2+x+1)(x^2+x)+(x^2+x+1)$
$=(x^2+x+1)[(x-1)(x^2+x)+1]$
$=(x^2+x+1)(x^3-x+1)$
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(4x^2-49=\left(2x\right)^2-7^2=\left(2x-7\right)\left(2x+7\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
`x^3 - 5x^2 + 8x + 4`
`= x^3 + x^2 + 4x^2 + 4x + 4x + 4`
`= x^2(x + 1) + 4x(x + 1) + 4(x + 1)`
`= (x + 1)(x^2 + 4x 4)`
`= (x + 1)(x + 2)^2`
(y^2+x*y+x^2)*(y^3-x^2*y+x^3)