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. 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, \(25x^2+5xy+\frac{1}{4}y^2=\left(5x\right)^2+2.5x.\frac{1}{2}y+\left(\frac{1}{2}y\right)^2\)

\(=\left(5x+\frac{1}{2}y\right)^2\)

b, \(9x^2+12x+4=\left(3x\right)^2+2.3x.2+2^2=\left(3x+2\right)^2\)

c, \(x^2-6x+5-y^2-4y=\left(x^2-6x+9\right)-\left(y^2+4y+4\right)\)

\(=\left(x-3\right)^2-\left(y+2\right)^2=\left(x-y-5\right)\left(x+y-1\right)\)

d, \(\left(2x-y\right)^2+4\left(x+y\right)^2-4\left(2x-y\right)\left(x+y\right)\)

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

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

Có cái cc

a) ( 2x + 1 )² + 10( 2x + 1 ) + 25

= ( 2x + 1 )² + 2.( 2x + 1 ).5 + 5²

= [ ( 2x + 1 ) + 5 ]²

= ( 2x + 1 + 5 )²

= ( 2x + 6 )²

b) x² + 2x( y - 2 ) + y² - 4y + 4

= x² + 2x( y - 2 ) + ( y² - 4y + 4 )

= x² + 2x( y - 2 ) + ( y - 2 )²

= [ x + ( y - 2 ) ]²

= ( x + y - 2 )²

c) x² + 12x + 40 + y² + 4y

= ( x² + 12x + 36 ) + ( y² + 4y + 4 )

= ( x + 6 )² + ( y + 2 )² ( cấy ni không viết được ;-; )

d) x² - 8x - 20 - y² - 12y

= ( x² - 8x + 16 ) - ( y² + 12y + 36 ) 

= ( x - 4 )² - ( y + 6 )²

= [ ( x - 4 ) - ( y + 6 ) ][ ( x - 4 ) + ( y + 6 ) ]

= ( x - 4 - y - 6 )( x - 4 + y + 6 )

= ( x - y - 10 )( x + y + 2 ) 

e) x² + y² + 4x + 4y + 2( x + 2 )( y + 2 ) + 8 

= ( x² + 4x + 4 ) + 2( x + 2 )( y + 2 ) + ( y² + 4y + 4 )

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

= [ ( x + 2 ) + ( y + 2 ) ]²

= ( x + 2 + y + 2 )²

= ( x + y + 4 )²

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

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

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

a, \(y^2-2y+1=y^2-y-y+1\\ =y.\left(y-1\right)-\left(y-1\right)=\left(y-1\right)^2\)

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

c, \(x^2-6x+9=x^2-3x-3x+9\\ =x.\left(x-3\right)-3.\left(x-3\right)=\left(x-3\right)^2\)

d, \(4y^2+4y+1=4y^2+2y+2y+1\\ =2y.\left(2y+1\right)+\left(2y+1\right)=\left(2y+1\right)^2\)

Mấy câu còn lại làm tương tự!

e, \(9a^2+6ab+b^2=9a^2+3ab+3ab+b^2\\ =3a.\left(3a+b\right)+b.\left(3a+b\right)=\left(3a+b\right)^2\)

g, \(4x^2+12xy+9y^2=4x^2+6xy+6xy+9y^2\\ =2x.\left(2x+3y\right)+3y.\left(2x+3y\right)=\left(2x+3y\right)^2\)

f, \(y^2-y+\dfrac{1}{4}=y^2-\dfrac{1}{2}y-\dfrac{1}{2}y+\dfrac{1}{4}\\ =y.\left(y-\dfrac{1}{2}\right)-\dfrac{1}{2}.\left(y-\dfrac{1}{2}\right)=\left(y-\dfrac{1}{2}\right)^2\)

Chúc bạn học tốt!!!

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

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

c/ \(x^2-6x+9=x^2-2\cdot x\cdot3+3^2=\left(x-3\right)^2\)

d/ \(4y^2+4y+1=\left(2y\right)^2+2\cdot2y\cdot1+1^2=\left(2y+1\right)^2\)

e/ \(9a^2+6ab+b^2=\left(3a\right)^2+2\cdot3a\cdot b+b^2=\left(3a+b\right)^2\)

g/ \(4x^2+12xy+9y^2=\left(2x\right)^2+2\cdot2x\cdot3y+\left(3y\right)^2=\left(2x+3y\right)^2\)

f/ \(y^2-y+\dfrac{1}{4}=y^2-2\cdot y\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(y^2-\dfrac{1}{2}\right)^2\)

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

b             \(4y^2+y+\frac{1}{16}=\left(2y\right)^2+2.2y.\frac{1}{4}+\left(\frac{1}{4}\right)^2=\left(2y+\frac{1}{4}\right)^2\)