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
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)
By Mackenzie
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 2x4−32=2(x4−24)=2(x−2)(x3−23)=2(x−2)(x−2)(x2+2x+4)
`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