Phân tích thành nhân tử: a) x^4y^4+4 b) 4x^4+1 c) 64x^4+1 d) x^4+64 e) 16x^4(x-y)-x+y f) 2x^3y-2xy^3-4xy^2-2xy g) x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2) h)

Question

Phân tích thành nhân tử:
a) x^4y^4+4
b) 4x^4+1
c) 64x^4+1
d) x^4+64
e) 16x^4(x-y)-x+y
f) 2x^3y-2xy^3-4xy^2-2xy
g) x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)
h) 16x^3-54y^3
i) 5x^2-5y^2
k) 16x^3y+1/4yz^3
l) 2x^4-32

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Mackenzie 2 tháng 2021-08-23T06:21:43+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-08-23T06:23:09+00:00

    Đáp án:

    a;= (x2y2 – 2xy + 2)(x2y2 + 2xy + 2)

     

    Giải thích các bước giải:

     a;x4y4 + 4

    = x4y4 + 4x2y2 + 4 – 4x2y2

    = (x2y2 + 2)2 – (2xy)2

    = (x2y2 – 2xy + 2)(x2y2 + 2xy + 2)
    b+d: mình gửi ảnh nhé
    c: mk cx gửi ảnh
    e+f+g ảnh nhé
    h+i ảnh
    k 2x432=2(x424)=2(x2)(x323)=2(x2)(x2)(x2+2x+4)

    0
    2021-08-23T06:23:40+00:00

    `a) x^4y^4+4`

    `=x^4y^4+4x^2y^2+4-4x^2y^2`

    `=(x^4y^4+4x^2y^2+4)-4x^2y^2`

    `=(x^2y^2+2)^2-4x^2y^2`

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

    `b) 4x^4+1`

    `=4x^4+4x^2+1-4x^2`

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

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

    `=(2x^2+1-2x)(2x^2+1+2x)`

    `c) 64x^4+1`

    `=64x^4+16x^2+1-16x^2`

    `=(64x^4+16x^2+1)-16x^2`

    `=(8x^2+1)^2-8x^2`

    `=(8x^2+1+4x)(8x^2+1-4x)`

    `d) x^4+64`

    `=x^4+16x^2+64-16x^2`

    `=(x^4+16x^2+64)-16x^2`

    `=(x^2+8)^2-16x^2`

    `=(x^2+8+4x)(x^2+8-4x)`

    `e) 16x^4(x-y)-x+y`

    `=16x^4(x-y)-(x-y)`

    `=(x-y)(16x^4-1)`

    `=(x-y)(4x^2+1)(4x^2-1)`

    `f) 2x^3y-2xy^3-4xy^2-2xy`

    `=2xy(x^2-y^2-2y-1)`

    `=2xy[x^2-(y^2+2y+1)]`

    `=2xy[x^2-(y+1)^2]`

    `=2xy(x+y+1)[x-(y+1)]`

    `=2xy(x+y+1)(x-y-1)`

    `g)``x(y^2- z^2)+y(z^2- x^2)+ z(x^2- y^2)`

    `=“x(y^2- z^2)+y(y^2 + z^2- x^2- y^2)+z(x^2 -y^2)`

    `=x(y^2-z^2)-y(y^2-z^2)-y(x^2-y^2)+z(x^2-y^2)“

    $=[x(y^2-z^2)-y(y^2-z^2)]+[-y(x^2-y^2)+z(x^2-y^2)]$

    `=(x-y)(y^2-z^2)-(y-z)(x^2-y^2)`

    `=(x-y)(y-z)(y+z)-(y-z)(x-y)(x+y)`

    `=(x-y)(y-z)[y+z-(x+y)]`

    `=(x-y)(y-z)(y+z-x-y)`

    `=(x-y)(y-z)(z-x)`

    `h) 16x^3-54y^3`

    `=2.(8x^3-27y^3)`

    `=2.(2x-3y)(4x^2+6xy+9y^2)`

    `i) 5x^2-5y^2`

    `=5(x^2-y^2)`

    `=5(x-y)(x+y)`

    `k) 16x^3y+1/4 yz^3`

    `=2y(8x^3+1/8 z^3)`

    `=2y(2x+1/2z)(4x^2+xz+1/4 z^2)`

    `l) 2x^4-32`

    `=2.(x^4-16)`

    `=2.(x^2 -4)(x^2 +4)`

    chúc học tốt

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