Phân tích đa thức sau thành nhân tử x²+2x+1-y² 4-y²+2y-1 x²-y²+2y-1 02/12/2021 Bởi Ayla Phân tích đa thức sau thành nhân tử x²+2x+1-y² 4-y²+2y-1 x²-y²+2y-1
Đáp án: `x^2 + 2x + 1 – y^2 = (x + 1 – y)(x + 1 + y)` `4 – y^2 + 2y – 1 = (y + 1)(3 – y)` `x^2 – y^2 + 2y – 1 = (x + y – 1)(x – y + 1)` Giải thích các bước giải: `x^2 + 2x + 1 – y^2` $\\$ `= (x^2 + 2x + 1) – y^2 ` $\\$ `= (x + 1)^2 – y^2 = (x + 1 – y)(x + 1 + y)` `4 – y^2 + 2y – 1 = 4 – (y^2 – 2y + 1) = 2^2 – (y – 1)^2 = (2 + y – 1)[2 – (y – 1)] = (y + 1)(2 – y + 1) = (y + 1)(3 – y)` `x^2 – y^2 + 2y – 1 = x^2 – (y^2 – 2y + 1) = x^2 – (y – 1)^2 = (x + y – 1)[x-(y – 1)] = (x + y – 1)(x – y + 1)` Bình luận
`\text{~~Holi~~}` `x^2+2x+1-y^2` `= (x+1)^2-y^2` `= (x+1-y)(x+1+y)` `4-y^2+2y-1` `= 4-(y-1)^2` `= (2+y-1)(2-y+1)` `x^2-y^2+2y-1` `= x^2-(y-1)^2` `= (x+y-1)(x-y+1)` Bình luận
Đáp án:
`x^2 + 2x + 1 – y^2 = (x + 1 – y)(x + 1 + y)`
`4 – y^2 + 2y – 1 = (y + 1)(3 – y)`
`x^2 – y^2 + 2y – 1 = (x + y – 1)(x – y + 1)`
Giải thích các bước giải:
`x^2 + 2x + 1 – y^2` $\\$ `= (x^2 + 2x + 1) – y^2 ` $\\$ `= (x + 1)^2 – y^2 = (x + 1 – y)(x + 1 + y)`
`4 – y^2 + 2y – 1 = 4 – (y^2 – 2y + 1) = 2^2 – (y – 1)^2 = (2 + y – 1)[2 – (y – 1)] = (y + 1)(2 – y + 1) = (y + 1)(3 – y)`
`x^2 – y^2 + 2y – 1 = x^2 – (y^2 – 2y + 1) = x^2 – (y – 1)^2 = (x + y – 1)[x-(y – 1)] = (x + y – 1)(x – y + 1)`
`\text{~~Holi~~}`
`x^2+2x+1-y^2`
`= (x+1)^2-y^2`
`= (x+1-y)(x+1+y)`
`4-y^2+2y-1`
`= 4-(y-1)^2`
`= (2+y-1)(2-y+1)`
`x^2-y^2+2y-1`
`= x^2-(y-1)^2`
`= (x+y-1)(x-y+1)`