bài 1:Phân tích đa thức thành nhân tử
1, A = x . (x – 1) + (1 – x)^2
2, A = (x + 1)^2 – 3 . (x + 1)
3, A = 2x . (x – 2) – (x – 2)^2
4, A = 3x . (x – 1)^2 – (1 – x)^3
5, A = 3x . (x + 2) – 5 . (x + 2)^2
6, A = 4x . (x – y) + 3 . (y – x)^2
giúp e với ạ!!
Đáp án:
1. `x(x – 1) + (1 – x)^2`
`= x(x – 1) + (x – 1)^2`
`= (x – 1)(x + x – 1)`
`= (x – 1)(2x – 1)`
2. `(x + 1)^2 – 3(x + 1)`
`= (x + 1)(x + 1 – 3)`
`= (x + 1)(x – 2)`
3. `2x(x – 2) – (x – 2)^2`
`= (x – 2)(2x – x + 2)`
`= (x – 2)(x + 2)`
4. `3x(x – 1)^2 – (1 – x)^3`
`= 3x(1 – x)^2 – (1 – x)^3`
`= (1 – x)^2(3x – 1 + x)`
`= (1 – x)^2(4x – 1)`
5. `3x(x + 2) – 5(x + 2)^2`
`= (x + 2)[3x – 5(x + 2)]`
`= (x + 2)(3x – 5x – 10)`
`= (x + 2)(-2x – 10)`
6. `4x .(x – y) + 3.(y – x)^2`
`= 4x(x – y) + 3(x – y)^2`
`= (x – y)[4x + 3(x – y)]`
`= (x – y)(4x + 3x – 3y)`
`= (x – y)(7x – 3y)`
Giải thích các bước giải: