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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, \(\left(2x-y\right)^2+4\left(x+y\right)^2-4\left(2x-y\right)\left(x+y\right)\)
\(=\left(2x-y\right)^2-2\left(2x-y\right)\left(2x+2y\right)+\left(2x+2y\right)^2\)
\(=\left(2x-y+2x+2y\right)^2=\left(4x+y\right)^2\)
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
\(a.x^2+x+\frac{1}{4}=x^2+2.x.\frac{1}{4}+\left(\frac{1}{4}\right)^2\)
\(=\left(x+\frac{1}{4}\right)^2\)
b) \(x^2+12xy+36xy^2=x^2+2.x.y+y^2\)
\(a.x^2+x+\frac{1}{4}=x^2+2.x.\frac{1}{4}+\left(\frac{1}{4}\right)^2\)
\(=\left(x+\frac{1}{4}\right)^2\)
b) \(x^2+12xy+36xy^2=x^2+2.x.y+y^2\)
\(a.x^2+x+\frac{1}{4}=x^2+2.x.\frac{1}{4}+\left(\frac{1}{4}\right)^2\)
\(=\left(x+\frac{1}{4}\right)^2\)
b) \(x^2+12xy+36xy^2=x^2+2.x.y+y^2\)
\(a.x^2+x+\frac{1}{4}=x^2+2.x.\frac{1}{4}+\left(\frac{1}{4}\right)^2\)
\(=\left(x+\frac{1}{4}\right)^2\)
b) \(x^2+12xy+36xy^2=x^2+2.x.y+y^2\)
d) \(x^2-2x+4=x^2-2.x.4+4^2\)
\(=\left(x-4\right)^2\)
e) \(25x^2+4y^2-20xy=\left(5x\right)^2-2.5x.2y+\left(2y\right)^2\)
\(=\left(5x-2y\right)^2\)
^...^ 
^_^ Bài làm có gì ko hiểu bạn cứ hỏi nhé ^_^
mạng của mk bị lỗi bạn xem cái phần cuối cùng nhé xl bạn nhiều vì mạng của mk bị lỗi 
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)\(36x^2+12xy+y^2\)
\(=\left(6x+y\right)^2\)
\(\left(2x-4y\right)^2+2\left(2x-4y\right)+1=\left(2x-4y+1\right)^2\)
(2x-4y)2+2(2x-4y)+1
=(2x-4y)2+2(2x-4y)+12
=(2x-4y+1)2