\(A=x^2+2y^2+2xy-2x+2\)

\(2A=2x^2+4y^2+4xy-4x+4\)

\(2A=x^2+4xy+4y^2+x^2-4x+4\)

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

\(A=\frac{\left(x+2y\right)^2+\left(x-2\right)^2}{2}\)

  9x²+4y²+2(3x+2y+6xy)+1

= 9x²+4y²+1+6x+4y+12xy

=(3x)²+(2y)²+1²+2.3x.2y+2.2y.1+2.3x.1   (1)

Thay 3x=m,2y=n,1=p

=>(1)=m²+n²+p²+2mn+2np+2pm=(m+n+p)²

=> 9x²+4y²+2(3x+2y+6xy)+1=(3x+2y+1)²

a)  \(x^2-4x+5+y^2+2y=\left(x^2-4x+4\right)+\left(y^2+2y+1\right)\)

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

b)  \(2x^2+y^2-2xy+10x+25=\left(x^2+10x+25\right)+\left(x^2-2xy+y^2\right)\)

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

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

bạn ơi , bạn lấy bài này ở đâu vậy bạn

tớ ko biết

a) \(M=2x^2+2y^2\)

\(=2x^2+2y^2+2xy-2xy\)

\(=x^2+2xy+y^2+x^2-2xy+y^2\)

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

b) \(N=a^2+16a+b^2+6b+73\)

\(=a^2+16a+64+b^2+6b+9\)

\(=\left(a+8\right)^2+\left(b+3\right)^2\)

cảm ơn bn

\(\left(\sqrt{2}x\right)^2+\left(\sqrt{2}y\right)^2\)

2x²+2y² = x²+y²+x²+y² = x²+2xy+y²+x²-2xy+y² = (x+y)² + (x-y)²

2x² + 2y² = 2(x² + y²)

\(2x^2+2y^2\)

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

Đặt nhân tử chung thôi 

T nha

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

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

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

c) Ta có: \(x^2-2x\left(y+2\right)+y^2+4y+4\)

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

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

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

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

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

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

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

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

\(\left(0,01+xy\right)^2=\frac{1}{10000}+\frac{1}{50}xy+x^2y^2\)

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

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

\(56.64=\left(60-4\right)\left(60+4\right)=60^2-4^2\)

tong la 2x²y²

(√2x)2+(√2y)2