Đáp án:
a, `x^4 - 4x^2 + 4x - 1`
` = (x^4 - 1) - (4x^2 - 4x)`
`= (x^2 - 1)(x^2 + 1) - 4x.(x - 1)`
`= (x - 1)(x + 1)(x^2 + 1) - 4x(x - 1)`
`= (x - 1)(x^3 + x^2 + x + 1 - 4x)`
`=(x - 1)(x^3 + x^2 - 3x + 1)`
`= (x - 1)[(x^3 + 2x^2 - x) - (x^2 + 2x - 1)]`
`= (x - 1)[x.(x^2 + 2x - 1) - (x^2 + 2x - 1)]`
`=(x - 1)(x - 1)(x^2 + 2x - 1)`
`= (x - 1)^2 . (x^2 + 2x - 1)`
b, `a(b^2 - c^2) + b(c^2 - a^2) + c(a^2 - b^2)`
` = a(b^2 - c^2) + bc^2 - ba^2 + ca^2 - cb^2`
` = a(b^2 - c^2) - (cb^2 - bc^2) - (ba^2 - ca^2)`
`= a(b - c)(b + c) - bc.(b - c) - a^2 . (b - c)`
` = (b - c)(ab + ac - bc - a^2)`
`=(b - c)[(ac - bc) - (a^2 - ab)]`
`=(b - c)[c.(a - b) - a.(a - b)]`
`=(b - c)(c - a)(a - b)`
c, `x^4 + 4`
` = (x^4 + 4x^2 + 4) - 4x^2`
`= (x^2 + 2)^2 - (2x)^2`
`= (x^2 - 2x + 2)(x^2 + 2x + 2)`
Giải thích các bước giải:
