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1: \(\left(x^2+1\right)^2-4x\left(1-x^2\right)\)

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

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

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

2: \(\left(x^2-8\right)^2+36\)

\(=x^4-16x^2+64+36\)

\(=x^4-16x^2+100\)

\(=x^4+20x^2+100-36x^2\)

\(=\left(x^2+10\right)^2-\left(6x\right)^2\)

\(=\left(x^2+6x+10\right)\left(x^2-6x+10\right)\)

3: \(x^4+4=x^4+4x^2+4-4x^2\)

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

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

4: \(x^4+64=x^4+16x^2+64-16x^2\)

\(=\left(x^2+8\right)^2-16x^2\)

\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)

5: \(64x^4+1=64x^4+16x^2+1-16x^2\)

\(=\left(8x^2+1\right)^2-16x^2\)

\(=\left(8x^2-4x+1\right)\left(8x^2+4x+1\right)\)

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)

29 tháng 6 2019

a) \(x^2+12x+35\)

\(=x^2+5x+7x+35\)

\(=\left(x^2+5x\right)+\left(7x+35\right)\)

\(=x\left(x+5\right)+7\left(x+5\right)\)

\(=\left(x+5\right)\left(x+7\right)\)

b)\(x^2-x-56\)

\(=x^2+7x-8x-56\)

\(=\left(x^2+7x\right)-\left(8x+56\right)\)

\(=x\left(x+7\right)-8\left(x+7\right)\)

\(=\left(x+7\right)\left(x-8\right)\)

c)\(5x^2-x-4\)

\(=5x^2-5x+4x-4\)

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

\(=5x\left(x-1\right)+4\left(x-1\right)\)

\(=\left(x-1\right)\left(5x+4\right)\)

29 tháng 6 2019

TL:

a)\(x^2+5x+7x+35\) 

 =\(x\left(x+5\right)+7\left(x+5\right)\) 

=\(\left(x+7\right)\left(x+5\right)\) 

b) \(x^2-x-56\)

  =\(x^2+7x-8x-56\) 

=\(x\left(x+7\right)-8\left(x+7\right)\) 

=\(\left(x-8\right)\left(x+7\right)\) 

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

=\(\left(2x^2+1\right)^2-4x^2\) 

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

.......................(tự lm)

hc tốt

25 tháng 9 2017

Ta có : x3 - 7x + 6 

= x3 - x - 6x + 6 

= x(x2 - 1) - 6(x - 1)

= x(x + 1)(x - 1) - 6(x - 1)

= (x - 1) [x(x + 1) - 6]

= (x - 1) (x2 + x - 6) . 

CÁC Ý SAU TƯƠNG TỰ

19 tháng 2 2018

   x3 - 7x + 6 

= x3 - x - 6x + 6 

= x(x2 - 1) - 6(x - 1)

= x(x + 1)(x - 1) - 6(x - 1)

= (x - 1) [x(x + 1) - 6]

= (x - 1) (x2 + x - 6) . 

26 tháng 12 2018

tự làm

1: =(x+y-3x)(x+y+3x)

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

2: =(3x-1-4)(3x-1+4)

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

=3(x+1)(3x-5)

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

=-[(x^2+1)^2-(2x)^2]

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

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

4: =(2x+1+x-1)(2x+1-x+1)

=3x(x+2)

5: =[(x+1)^2-(x-1)^2][(x+1)^2+(x-1)^2]

=(2x^2+2)*4x

=8x(x^2+1)

6: =(5x-5y)^2-(4x+4y)^2

=(5x-5y-4x-4y)(5x-5y+4x+4y)

=(x-9y)(9x-y)

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

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

=(x+y)^3*(x-y)

8: =(x^2+4y^2-20-4xy+16)(x^2+4y^2-20+4xy-16)

=[(x-2y)^2-4][(x+2y)^2-36]

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

a: =64x^4+16x^2y^2+y^4-16x^2y^2

=(8x^2+y^2)^2-(4xy)^2

=(8x^2+y^2-4xy)(8x^2+y^2+4xy)

b: =x^8+2x^4+1-x^4

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

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

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

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

c: =(x+1)(x^2-x+1)+2x(x+1)

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

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

d: =(x^2-1)(x^2+1)-2x(x^2-1)

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

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

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

16 tháng 10 2016

hoa mắt chóng mặt

16 tháng 10 2016

Nhờ bạn làm cho mik ít câu cũng dc