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x4 + 4
= (x2)2 + 22
= x4 + 2.x2.2 + 4 – 4x2
(Thêm bớt 2.x2.2 để có HĐT (1))
= (x2 + 2)2 – (2x)2
(Xuất hiện HĐT (3))
= (x2 + 2 – 2x)(x2 + 2 + 2x)
![](https://rs.olm.vn/images/avt/0.png?1311)
Sửa đề: x^4+4y^4
=x^4+4x^2y^2+4y^4-4x^2y^2
=(x^2+2y^2)^2-4x^2y^2
=(x^2-2xy+2y^2)(x^2+2xy+2y^2)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{a) }4x^{16}+81=4x^4+36x^2+81-36x^8\)
\(=\left(4x^{16}+36x^8+81\right)-36x^8\)
\(=\left[\left(2x^8\right)^2+2.2x^8.9+9^2\right]+\left(6x^4\right)^2\)
\(=\left(2x^8+9\right)^2-\left(6x^4\right)^2\)
\(=\left(2x^8+9-6x^4\right)\left(2x^8+9+6x^4\right)\)
\(\text{b) }x^4+2018x^2+2017x+2018\)
\(=x^4+2018x^2+2018x-x+2018\)
\(=\left(x^4-x\right)+\left(2018x^2+2018x+2018\right)\)
\(=x\left(x^3-1\right)-2018\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2018\left(x^2+x+1\right)\)
\(=\left(x^2-x\right)\left(x^2+x+1\right)+2018\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2018\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : x4 + 2018x2 + 2017x + 2018
= x4 - x + 2018x2 + 2018x + 2018
= x(x3 - 1) + 2018(x2 + x + 1)
= x(x - 1)(x2 + x + 1) + 2018(x2 + x + 1)
= (x2 + x + 1)(x2 - x + 2018)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : x^4+2017x^2+2016x+2017
=x^4+x^3-x^3+x^2-x^2+2017x^2+2017x-x+2017
=x^4+x^3+x^2-x^3-x^2-x+2017x^2+2017x+2017
=x^2(x^2+x+1)-x(x^2+x+1)+2017(x^2+x+1)
=(x^2+x+1)(x^2-x+2017)
Nhớ k mk nha
Ta có : x^4+2017x^2+2016x+2017
=x^4+x^3-x^3+x^2-x^2+2017x^2+2017x-x+2017
=x^4+x^3+x^2-x^3-x^2-x+2017x^2+2017x+2017
=x^2(x^2+x+1)-x(x^2+x+1)+2017(x^2+x+1)
=(x^2+x+1)(x^2-x+2017)
chúc cậu hok tốt _@
![](https://rs.olm.vn/images/avt/0.png?1311)
x 4 - 2 x 3 - 2 x 2 - 2 x - 3 = ( x 4 − 1 ) − ( 2 x 3 + 2 x 2 ) − ( 2 x + 2 ) = ( x 2 + 1 ) ( x 2 − 1 ) − 2 x 2 ( x + 1 ) − 2 ( x + 1 ) = ( x 2 + 1 ) ( x − 1 ) ( x + 1 ) − 2 x 2 ( x + 1 ) − 2 ( x + 1 ) = ( x + 1 ) ( x 2 + 1 ) ( x − 1 ) − 2 x 2 – 2 = ( x + 1 ) ( x 2 + 1 ) ( x − 1 ) − 2 ( x 2 + 1 ) = ( x + 1 ) ( x 2 + 1 ) ( x – 1 − 2 ) = ( x + 1 ) ( x 2 + 1 ) ( x − 3 )
x^4 - 2x^3 - 2x^2 - 2x - 3
= x^4 - 1 - 2x^3 - 2x^2 - 2x -2
= ( x - 1 ) ( x + 1 ) ( x^2 + 1 ) - 2x^2 ( x + 1 ) - 2 ( x + 1 )
= ( x + 1 ) [ ( x - 1 ) ( x^2 + 1 ) - 2x^2 - 2 ]
= ( x + 1 ) [ ( x - 1 ) ( x^2 + 1 - 2 ( x^2 - 1 ) ]
= ( x + 1 ) [ ( x - 1 ) ( x^2 + 1 ) - 2 ( x - 1 ) ( x + 1 ) ]
= ( x + 1 ) ( x - 1 ) [ ( x^2 + 1 ) - 2 ( x +1 )
= ( x + 1 ) ( x - 1 ) ( x^2 +1 - 2x - 2 )
= ( x + 1 ) ( x - 1 ) ( x^2 - 2x - 1 )
![](https://rs.olm.vn/images/avt/0.png?1311)
d) x4 + 2x3 - 4x – 4 = (x4 – 4) + (2x3 – 4x) = (x2 – 2)(x2 + 2) + 2x(x2 – 2)
= (x2 – 2)(x2 + 2 + 2x) = (x - √2)( x + √2)( x2 + 2 + 2x)
x4+2018x2+2017x+2018=x4+2018x2+2018x-x+2018
=x(x3-1)+2018(x2+x+1)=(x2+x+1)(x2-x+2018)
Ktra xem mk có nhầm chỗ nào ko nhé. Cảm ơn bạn
ko có j