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24 tháng 7 2017

a, 1-2x+x^2 = x^2 - 2x.1 + 1^2= (x-1)^2

b, 4y+4+y^2 = y^2 + 2y.2+ 2^2 = (y+2)^2

c, 1/16+1/2x+x^2 = x^2 + 2.x.\(\frac{1}{4}\)+ (1/4)^2 = (x+1/4)^2

d, 36x^2+12xy+y^2 = (6x)^2 + 2.6x.y + y^2 = (6x+y)^2

24 tháng 7 2017

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

b) \(4y+4+y^2=y^2+4y+4=\left(y+2\right)^2\)

c) \(\frac{1}{16}+\frac{1}{2}x+x^2=\left(x+\frac{1}{4}\right)^2\)

d) \(36x^2+12xy+y^2=\left(6x+y\right)^2\)

22 tháng 7 2017

A)\(1-2x+x^2\)

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

B)\(4y+4+y^2\)

\(=2^2+4y+y^2\)

\(=\left(2+y\right)^2\)

C)\(\frac{1}{16}+\frac{1}{2}x+x^2\)

\(=\left(\frac{1}{4}\right)^2+\frac{1}{2}x+x^2\)

\(=\left(\frac{1}{4}+x\right)\)

D)\(36x^2+12xy+y^2\)

\(=\left(6x+y\right)^2\)

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)

25 tháng 10 2021

\(a,=\left(x^2y+3\right)^2\\ b,=\left(2x+y\right)^2\\ c,=\left(5y^2-1\right)^2\)

25 tháng 10 2021

a) \(6x^2y+9+x^4y^2=\left(x^2y+3\right)^2\)

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

c) \(25y^4-10y^2+1=\left(5y^2-1\right)^2\)

a) Ta có: \(\left(x^2+9x+18\right)^2+2\left(x^2+9x\right)+37\)

\(=\left(x^2+9x+18\right)^2+2\cdot\left(x^2+9x+18\right)-36+37\)

\(=\left(x^2+9x+19\right)^2\)

b) Ta có: \(x^2+y^2+2x+2y+2\left(x+1\right)\left(y+1\right)+2\)

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

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

23 tháng 6 2023

này mình có vài câu không làm được, xin lỗi bạn nha

\(b,16x^2-8x+1=\left(4x-1\right)^2\\ c,4x^2+12xy+9y^2=\left(2x+3y\right)^2\\ e,=x^2+2x+1+y^2+2y+1+2\left(x+1\right)\left(y+1\right)\\ =\left(x+1\right)^2+2\left(x+1\right)\left(y+1\right)+\left(y+1\right)^2\\ =\left[\left(x+1\right)+\left(y+1\right)\right]^2=\left(x+y+2\right)^2\\ g,=x^2-2x\left(y+2\right)+\left(x+2\right)^2=\left[x-\left(y+2\right)\right]^2=\left(x-y-2\right)^2\\ h,=\left[x+\left(y+1\right)\right]^2=\left(x+y+1\right)^2\)

 

 

 

 

 

 

12 tháng 10 2021

Bài 2: 

a: \(3x^2-3xy=3x\left(x-y\right)\)

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

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

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

18 tháng 10 2021

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19 tháng 9 2021

\(a,=\left(x-4\right)^2\\ b,=\left(\dfrac{1}{2}xy^2+1\right)^2\)

a: Ta có: \(\left(x+3\right)\left(x+4\right)\left(x+5\right)\left(x+6\right)+1\)

\(=\left(x^2+9x+18\right)\left(x^2+9x+20\right)+1\)

\(=\left(x^2+9x\right)^2+38\left(x^2+9x\right)+360+1\)

\(=\left(x^2+9x\right)^2+2\cdot\left(x^2+9x\right)\cdot19+19^2\)

\(=\left(x^2+9x+19\right)^2\)

24 tháng 8 2021

b. \(x^2+y^2+2x+2y+2\left(x+1\right)\left(y+1\right)+2\)

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

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

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

c. \(x^2-2x\left(y+2\right)+y^2+4y+4\)

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

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

d. \(x^2+2x\left(y+1\right)+y^2+2y+1\)

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

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

21 tháng 9 2021

\(1,\\ a,=x^2+2xy+y^2\\ b,=x^2-4xy+4y^2\\ c,=x^2y^4-1\\ d,=\left[\left(x-y\right)\left(x+y\right)\right]^2=\left(x^2-y^2\right)^2=x^4-2x^2y^2+y^4\\ 2,\\ a,=\left(x+2\right)^2\\ b,=\left(3x-2\right)^2\\ c,=\left(\dfrac{x}{2}+1\right)^2\\ d,=\left(x+y-2\right)^2\)

21 tháng 9 2021

Bài 1 em dùng HĐT nha

Bài 2:

a. x2 + 4x + 4

= x2 + 2.2.x + 22

= (x + 2)2

b. 9x2 - 12x + 4

= (3x)2 - 3x.2.2 + 22

= (3x - 2)2

c. \(\dfrac{x^2}{4}+x+1\)

\(\left(\dfrac{x}{2}\right)^2+2.\dfrac{x}{2}.1+1^2\)

\(\left(\dfrac{x}{2}+1\right)^2\)