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4 tháng 8 2018

b,\(\dfrac{4}{9}x^2+4x+9=\left(\dfrac{2}{3}x\right)^2+2.\dfrac{2}{3}x.3+3^2=\left(\dfrac{2}{3}x+3\right)^2\)

c, \(x^3+9x^2+27x+27=x^3+3.x^2.3+3.x.3^2+3^3=\left(x+3\right)^3\)

d, \(\dfrac{1}{8}-\dfrac{3}{4}x+\dfrac{3}{2}x^2-x^3=\left(\dfrac{1}{2}\right)^3-3.\left(\dfrac{1}{2}\right)^2.x+3.\dfrac{1}{2}.x^2-x^3=\left(\dfrac{1}{2}-x\right)^3\)

TK MIK vui

29 tháng 6 2023

1, \(x^2+2xy+y^2=\left(x+y\right)^2\)

2, \(4x^2+12x+9=\left(2x\right)^2+2\cdot3\cdot2x+3^2=\left(2x+3\right)^2\)

3, \(x^2+5x+\dfrac{25}{4}=x^2+2\cdot\dfrac{5}{2}\cdot x+\left(\dfrac{5}{2}\right)^2=\left(x+\dfrac{5}{2}\right)^2\)

4, \(16x^2-8x+1=\left(4x\right)^2-2\cdot4x\cdot1+1^2=\left(4x-1\right)^2\)

5, \(x^2+x+\dfrac{1}{4}=x^2+2\cdot\dfrac{1}{2}\cdot x+\left(\dfrac{1}{2}\right)^2=\left(x+\dfrac{1}{2}\right)^2\)

1: =(x+y)^2

2: =(2x+3)^2

3: =(x+5/2)^2

4: =(4x-1)^2

5: =(x+1/2)^2

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

7: =(x+1)^3

8: =(1/2x+1)^2

9: =(3y-1/3)^3

10: =(2x+y)^3

27 tháng 10 2023

a. $x^2+4x+4$

$=x^2+2\cdot x\cdot2+2^2$

$=(x+2)^2$

b. $x^2-6xy+9y^2$

$=x^2-2\cdot x\cdot3y+(3y)^2$

$=(x-3y)^2$

c. $4x^2+12x+9$

$=(2x)^2+2\cdot2x\cdot3+3^2$

$=(2x+3)^2$

d. $x^2-x+\dfrac14$

$=x^2-2\cdot x\cdot \dfrac12+\Bigg(\dfrac12\Bigg)^2$

$=\Bigg(x-\dfrac12\Bigg)^2$

27 tháng 10 2023

`x^2 +4x+4`

`=x^2+2*x*2+2^2`

`=(x+2)^2`

__

`x^2-6xy+9y^2`

`=x^2 - 2*x*3y+(3y)^2`

`=(x-3y)^2`

__

`4x^2 +12x+9`

`=(2x)^2 +2*2x*3+3^2`

`=(2x+3)^2`

__

`x^2-x+1/4`

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

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

25 tháng 9 2021

\(\dfrac{x^2}{4}-3x+9=\left(\dfrac{x}{2}-3\right)^2\)

30 tháng 9 2021

a)
=(x-2)3
b)\(\left(2-x\right)^3\)
c)\(\left(x+\dfrac{1}{3}\right)^3\)
d)\(\left(\dfrac{x}{2}+y\right)^3\)
e)
\(=\left(x-1\right)^2\left(x-1-15\right)+25\left[3\left(x-1\right)-5\right]\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-3-5\right)\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-8\right)\)
 

22 tháng 7 2023

a) \(x^2+2x+1\)

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

b) \(9-24x+16x^2\)

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

c) \(4x^2+\dfrac{1}{4}+2x\)

\(=4x^2+2x+\dfrac{1}{4}\)

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

2:

a: a^2-b^2

b: (a-b)^2

c: 1/2(a^2+b^2)

d: 1/2(a^3+b^3)

25 tháng 7 2017

a)\(x^2+4x+4=x^2+2\cdot2\cdot x+2^2=\left(x+2\right)^2\)

b)\(9x^2+42x+49=\left(3x\right)^2+2\cdot3x\cdot7+7^2=\left(3x+7\right)^2\)

c)\(\dfrac{1}{9}-\dfrac{2}{3}y^4+y^8=\left(\dfrac{1}{3}\right)^2-2\cdot\dfrac{1}{3}\cdot y^4+\left(y^4\right)^2=\left(y^4-\dfrac{1}{3}\right)^2\)

25 tháng 7 2017

a) \(x^2+2.2x+2^2\)

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

b)\(\left(3x\right)^2+2.3.7x+7^2\)

\(=\left(3x+7\right)^2\)

c) \(\left(\dfrac{1}{3}\right)^2-2.\dfrac{1}{3}.y^4+\left(y^4\right)^2\)

\(=\left(\dfrac{1}{3}-y^4\right)^2\)

19 tháng 9 2021

\(a,=\left(x+\dfrac{5}{2}\right)^2\\ b,=\left(2x+3y\right)^2\\ c,=a^2+b^2+c^2+2ab-2bc-2ac\\ d,=\left(4x-1\right)^2\\ e,=a^2+b^2+c^2+2ab+2bc+2ac\\ f,=a^2+b^2+c^2-2ab+2bc-2ac\)