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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: phân tích đa thức thành nhân tử 1, 4x^2-y162+4x+1 2,x^3-x+y^3-y 3,x^2-x-y^2-y 4,x^2-2xy+y^2-z^2 5,x^4+2x^3+x^2

Toán Lớp 8: phân tích đa thức thành nhân tử
1, 4x^2-y162+4x+1
2,x^3-x+y^3-y
3,x^2-x-y^2-y
4,x^2-2xy+y^2-z^2
5,x^4+2x^3+x^2

Comments ( 2 )

  1. 1)
    4x^2 – 16y^2 + 4x + 1
    = (4x^2 + 4x + 1) – 16y^2
    = (2x+1)^2 – (4y)^2
    = (2x+1 – 4y)(2x+1+4y)
    2)
    x^3 – x + y^3 – y
    = (x^3 + y^3) – (x+y)
    =  (x+y)(x^2 – xy + y^2) – (x+y)
    =  (x+y) (x^2 – xy  + y^2 – 1)
    3)
    x^2 – x – y^2 – y
    = (x^2 – y^2) – (x+y)
    = (x+y)(x-y) – (x+y)
    = (x+y)(x-y-1)
    4)
    x^2 – 2xy + y^2 – z^2
    =(x^2 -2xy+y^2)-z^2
    = (x-y)^2 – z^2
    = (x-y-z)(x-y+z)
    5)
    x^4 + 2x^3 + x^2
    = x^2 (x^2 + 2x + 1)
    = x^2 (x+1)^2
     

  2. 1)4x^2-y^2+4x+1
    =(4x^2+4x+1)-y^2
    =[(2x)^2+2.2x.1+1^2]-y^2
    =(2x+1)^2-y^2
    =(2x+1-y)(2x+1+y)
    2)x^3-x+y^3-y
    =(x^3+y^3)-(x+y)
    =(x+y)(x^2-xy+y^2)-(x+y)
    =(x+y)(x^2-xy+y^2-1)
    3)x^2-x-y^2-y
    =(x^2-y^2)-(x+y)
    =(x-y)(x+y)-(x+y)
    =(x+y)-(x-y-1)
    4)x^2-2xy+y^2-z^2
    =(x^2-2xy+y^2)-x^2
    =(x-y)^2-x^2
    =(x-y-z)(x-y+z)
    5)x^4+2x^3+x^2
    =x^2(x^2+2x+1)
    =x^2(x+1)^2
     

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222-9+11+12:2*14+14 = ? ( )