Lời giải:

a. $-8x+16+x^2=x^2-2.x.4+4^2=(x-4)^2$

b. $xy^2+\frac{1}{4}x^2y^4+1=(\frac{1}{2}xy^2)^2+2.\frac{1}{2}xy^2.1+1^2$

$=(\frac{1}{2}xy^2+1)^2$

a: \(x^2-8x+16=\left(x-4\right)^2\)

b: \(\dfrac{1}{4}x^2y^4+xy^2+1=\left(\dfrac{1}{2}xy^2+1\right)^2\)

a. x² + 6x + 9 = (x + 3)²

b. 25 + 10x + x² = (5 + x)²

c. x² + 8x + 16 = (x + 4)²

d. x² + 14x + 49 = (x + 7)²

e. 4x² + 12x + 9 = (2x + 3)²

f. 9x² + 12x + 4 = (3x + 2)²

h. 16x² + 8 + 1 = (4x + 1)²

i. 4x² + 12xy + 9y² = (2x + 3y)²

k. 25x² + 20xy + 4y² = (5x + 2y)²

a) \(=\left(x+3\right)^2\)

b) \(=\left(x+5\right)^2\)

c) \(=\left(x+4\right)^2\)

d) \(=\left(x+7\right)^2\)

e) \(=\left(2x+3\right)^2\)

f) \(=\left(3x+2\right)^2\)

h) \(=\left(4x+1\right)^2\)

i) \(=\left(2x+3y\right)^2\)

k) \(=\left(5x+2y\right)^2\)

a) ( x   +   1 ) 2 .                     b) ( x   –   4 ) 2 .

c) x 2 4 + x + 1 ;                   d) ( 2 x   –   2 y ) 2 .

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

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

`a)x^2+20x+100=(x+10)^2`

`b)16x^2+24xy+9y^2=(4x+3y)^2`

`c)y^2-14y+49=(y-7)^2`

`d)9x^2-42xy+49y^2=(3x-7y)^2`

a, \(x^2+2x.10+100=\left(x+10\right)^2\)

\(b,16x^2+2.4x.3y+9y^2=\left(4x+3y\right)^2\)

\(c,y^2-14y+49=\left(y-7\right)^2\)

\(d,9x^2-2.3x.7x+49y^2=\left(3x-7y\right)^2\)

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

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. \(\dfrac{x^2}{4}+x+1\)

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

= \(\left(\dfrac{x}{2}+1\right)^2\) 

\(a,\)

với \(a=100\)

\(=>9x^2+30x+25=\left(3x\right)^2+2.3.5x+5^2=\left(3x_{ }+5\right)^2\)

\(b,\)

với \(a=\dfrac{1}{25}\)

\(25x^2-2x+\dfrac{1}{25}=\left(5x\right)^2-2.5.x.\dfrac{1}{5}+\left(\dfrac{1}{5}\right)^2=\left(5x-\dfrac{1}{5}\right)^2\)

\(c,\)

với  \(a=6\)

\(=>x^2+2.3.x+3^2=\left(x+3\right)^2\)

\(d.\)

với \(a=\dfrac{4}{3}\)

\(=>\left(2x\right)^2-2.2.\dfrac{1}{3}x+\left(\dfrac{1}{3}\right)^2=\left(2x-\dfrac{1}{3}\right)^2\)

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

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

7, \(x^3+3x^2+3x+1=x^3+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3=\left(x+1\right)^3\)

8, \(\dfrac{x^2}{4}+x+1=\left(\dfrac{x}{2}\right)^2+2\cdot\dfrac{x}{2}\cdot1+1^2=\left(\dfrac{x}{2}+1\right)^2\)

9, \(27y^3-9y^2+y-\dfrac{1}{27}=\left(3y\right)^3-3\cdot\left(3y\right)^2\cdot\dfrac{1}{3}+3\cdot3y\cdot\left(\dfrac{1}{3}\right)^2-\left(\dfrac{1}{3}\right)^3=\left(3y-\dfrac{1}{3}\right)^3\)

10, \(8x^3+12x^2y+6xy^2+y^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2+y^3=\left(2x+y\right)^3\)

a) \(x^2-6x+9=x^2-2.3.x+3^2=\left(x-3\right)^2\)

b)\(x^2+4x+4=x^2+2.2.x+2^2=\left(x+2\right)^2\)

c)\(4x^2+4x+1=\left(2x\right)^2+2.2x.1+1^2=\left(2x+1\right)^2\)

d)\(4x^2+12xy+9y^2=\left(2x\right)^2+2.2x.3y+\left(3y\right)^2=\left(2x+3y\right)^2\)

e)\(x^2-8x+16=x^2-2.4.x+4^2=\left(x-4\right)^2\)

a) x² -6x +9 = (x-3)²                                       

b) x²+4x +4= (x+2)²

c) 4x²+4x+1= (2x+1)²

d) 4x²+12xy+9y² = (2x+3y)²

e) x²-8x+16 = (x-4)²

Đây chính là hằng đẳng thức nhé bn....