Question

[Ngoc Linh]

Phân tích các đa thức sau thành nhân tử:

 \(\left(4x-1\right)^2-121\)

\(x^6-y^6\)

Answer 1

[『Kuroba ム Tsuki Ryoo ︵²ᵏ⁷』]

`#3107.101107`

`(4x - 1)^2 - 121`

`= (4x - 1)^2 - (11)^2`

`= (4x - 1 - 11)(4x - 1 + 11)`

`= (4x - 12)(4x + 10)`

`= 4(x - 3) * 2(2x + 5)`

`= 8(x - 3)(2x + 5)`

_____

`x^6 - y^6`

`= (x^3)^2 - (y^3)^2`

`= (x^3 - y^3)(x^3 + y^3)`

`= (x - y)(x^2 + xy + y^2)(x + y)(x^2 - xy + y^2)`

`= (x - y)(x + y)(x^2 + xy + y^2)`

____

Sử dụng các HĐT:

`@` `A^2 - B^2 = (A - B)(A + B)`

`@` `A^3 - B^3 = (A - B)(A^2 + AB + B^2)`

`@` `A^3 + B^3 = (A + B)(A^2 - AB + B^2).`

Answer 2

[Nguyễn Lê Phước Thịnh]

a: \(\left(4x-1\right)^2-121\)

\(=\left(4x-1\right)^2-11^2\)

\(=\left(4x-1-11\right)\left(4x-1+11\right)\)

\(=\left(4x-12\right)\left(4x+10\right)\)

\(=8\left(x-3\right)\left(2x+5\right)\)

b: \(x^6-y^6\)

\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)