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3 tháng 8 2018

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25

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316

 nhớ cho mình 1 k

19 tháng 6 2015

a) x^2+2xy+y^2-16

=(x+y)2-16

=(x+y-4)(x+y+4)

b) 3x^2+5x-3xy-5y

=(3x2-3xy)+(5x-5y)

=3x(x-y)+5(x-y)

=(x-y)(3x+5)

c) 4x^2-6x^3y-2x^2+8x

ko bik hoặc sai đề

d) x^2-4-2xy+y^2

=(x-y)2-4

=(x-y+2)(x-y-2)

e) x^3-4x^2-12x+27

=sai đề

g) 3x^2-18x+27

=3(x2-6x+9)

=3(x-3)2

h) x^2-y^2-z^2-2yz

=x2-(y2+z2+2yx)

=x2-(y+z)2

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

k) 4x^2(x-6)+9y^2(6-x)

=4x2(x-6)-9y2(x-6)

=(x-6)(4x2-9y2)

=(x-6)(2x-3y)(2x+3y)

l)6xy+5x-5y-3x^2-3y^2

=(5x-5y)+(-3x2+6xy-3y2)

=5(x-y)-3(x2-2xy+y2)

=5(x-y)-3(x-y)2

=(x-y)(5-3(x-y))

=(x-y)(5-3x+3y)

3 tháng 8 2023

a) 9x4+16y6-24x2y3

=(3x2)2-2.3x2.4y3+(4y3)2

=(3x2-4y3)2

b) 16x2-24xy+9y2

=(4x)2-2.4x.3y+(3y)2

=(4x-3y)2

c) 36x2-(3x-2)2

=(36x-3x+2)(36x+3x-2)

=(33x+2)(39x-2)

d) 27x3+54x2y+36xy2+8y3

=(3x)3+3.(3x)2.2y+3.3x.(2y)2+(2y)3

=(3x+2y)3

e) y9-9x2y6+27x4y3-27x6

=(y3)3-3.(y3)2.3x2+3.y3.(3x2)2-(3x2)3

=(y3-3x2)3

f) 64x3+1

= (4x)3+13

=(4x+1)[(4x)2-4x.1+12]

=(4x+1)(16x2-4x+1)

e) 27x6-8x3  *sửa đề*

=(3x2)3-(2x)3

=(3x2-2x)[(3x)2+3x2.2x+(2x)2]

=(3x2-2x)(9x2+6x3+4x2)

~~~

6 tháng 4 2020

\(a.\left(8x^4-4x^3+x^2\right):2x^2=4x^2-2x+\frac{1}{2}\)

\(b.\left(2x^4-x^3+3x^2\right):\left(-\frac{1}{3x^2}\right)=-6x^6+3x^5-9x^4\)

\(c.\left(-18x^3y^5+12x^2y^2-6xy^3\right):6xy=-3x^2y^4+2xy-y^2\)

\(d.\left(\frac{3}{4x^3y^6}+\frac{6}{5x^4y^5}-\frac{9}{10x^5y}\right):-\frac{3}{5x^3y}=-\frac{5}{4y^5}-\frac{2}{xy^4}-\frac{3}{2x^2}\)

6 tháng 4 2020

Thank you

30 tháng 7 2023

1) \(4x^5y^2-8x^4y^2+4x^3y^2\)

\(=4x^3y^2\left(x^2-2x+1\right)\)

\(=4x^3y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

\(=4x^3y^2\left(x-1\right)^2\)

2) \(5x^4y^2-10x^3y^2+5x^2y^2\)

\(=5x^2y^2\left(x^2-2x+1\right)\)

\(=5x^2y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

\(=5x^2y^2\left(x-1\right)^2\)

3) \(12x^2-12xy+3y^2\)

\(=3\left(4x^2-4xy+y^2\right)\)

\(=3\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

\(=3\left(2x-y\right)^2\)

4) \(8x^3-8x^2y+2xy^2\)

\(=2x\left(4x^2-4xy+y^2\right)\)

\(=2x\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

\(=2x\left(2x-y\right)^2\)

5) \(20x^4y^2-20x^3y^3+5x^2y^4\)

\(=5x^2y^2\left(4x^2-4xy+y^2\right)\)

\(=5x^2y^2\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

\(=5x^2y^2\left(2x-y\right)^2\)

1: 4x^5y^2-8x^4y^2+4x^3y^2

=4x^3y^2(x^2-2x+1)

=4x^3y^2(x-1)^2

2: \(=5x^2y^2\left(x^2-2x+1\right)=5x^2y^2\left(x-1\right)^2\)

3: \(=3\left(4x^2-4xy+y^2\right)=3\left(2x-y\right)^2\)

4: \(=2x\left(4x^2-4xy+y^2\right)=2x\left(2x-y\right)^2\)

5: \(=5x^2y^2\left(4x^2-4xy+y^2\right)=5x^2y^2\left(2x-y\right)^2\)

16 tháng 12 2018

\(10x\left(x-y\right)-6y\left(y-x\right)\)

\(=10x\left(x-y\right)+6x\left(x-y\right)\)

\(=\left(10x+6x\right)\left(x-y\right)\)

\(c,3x^2+5y-3xy-5x\)

\(=\left(3x^2-3xy\right)+\left(5y-5x\right)\)

\(=3x\left(x-y\right)-5\left(x-y\right)\)

\(=\left(3x-5\right)\left(x-y\right)\)

\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)

16 tháng 12 2018

\(f,8x^3-12x^2y+6xy^2-y^3\)

\(=\left(2x-y\right)^3\)

\(g,x^3+8y^3=x^3+\left(2y\right)^3\)

\(=\left(x+2y\right)\left(x^2-2xy+4x^2\right)\)

\(i,x^2-25-2xy+y^2\)

\(\left(x^2-2xy+y^2\right)-25=\left(x-y\right)^2-5^2\)

\(=\left(x-y-5\right)\left(x-y+5\right)\)

a: =(6x)^2-(3x-2)^2

=(6x-3x+2)(6x+3x-2)

=(9x-2)(3x+2)

d: \(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)

\(=4x\cdot\left[x^2+2x+1+x^2-2x+1\right]\)

=8x(x^2+1)

e: =(4x)^2-2*4x*3y+(3y)^2

=(4x-3y)^2

f: \(=-\left(\dfrac{1}{4}x^4-2\cdot\dfrac{1}{2}x^2\cdot2y^3+4y^6\right)\)

\(=-\left(\dfrac{1}{2}x^2-2y^3\right)^2\)

g: =(4x)^3+1^3

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

k: =x^3(27x^3-8)

=x^3(3x-2)(9x^2+6x+4)

l: =(x^3-y^3)(x^3+y^3)

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

Bài 4:

a) Ta có: \(x^3+6x^2+12x+8\)

\(=x^3+2x^2+4x^2+8x+4x+8\)

\(=x^2\left(x+2\right)+4x\left(x+2\right)+4\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2+4x+4\right)\)

\(=\left(x+2\right)^3\)

b) Ta có: \(x^3-3x^2+3x-1\)

\(=x^3-x^2-2x^2+2x+x-1\)

\(=x^2\left(x-1\right)-2x\left(x-1\right)+\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2-2x+1\right)\)

\(=\left(x-1\right)^3\)

c) Ta có: \(1-9x+27x^2-27x^3\)

\(=1-3x-6x+18x^2+9x^2-27x^3\)

\(=\left(1-3x\right)-6x\left(1-3x\right)+9x^2\left(1-3x\right)\)

\(=\left(1-3x\right)\left(1-6x+9x^2\right)\)

\(=\left(1-3x\right)^3\)

d) Ta có: \(x^3+\frac{3}{2}x^2+\frac{3}{4}x+\frac{1}{8}\)

\(=x^3+3\cdot x^2\cdot\frac{1}{2}+3\cdot x\cdot\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3\)

\(=\left(x+\frac{1}{2}\right)^3\)

e) Ta có: \(27x^3-54x^2y+36xy^2-8y^3\)

\(=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot2y+3\cdot3x\cdot\left(2y\right)^2-\left(2y\right)^3\)

\(=\left(3x-2y\right)^3\)