## 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

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

1. 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)

2. 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)`

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