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

b) \(x^2+12xy+36y^2=\left(x+6y\right)^2\)

c) \(4x^2-12xy+9y^2=\left(2x-3y\right)^2\)

d) Không phải hằng đẳng thức \(\left(x^2-2x+4=\left(x-1\right)^2+3\right)\)

e) \(25x^2+4y^2-20xy=\left(5x-2y\right)^2\)

a) \(5x^2-12xy+9y^2-4x+4=\left(4x^2-12xy+9y^2\right)+x^2-4x+4=\left(2x-3y\right)^2+\left(x-2\right)^2\ge0\)
b) \(-x^2-2y^2+12x-4y+7=-\left(x^2-12x+36\right)-2\left(y^2+2y+1\right)+45=-\left(x-6\right)^2-2\left(y+1\right)^2+45\le45\)

c)\(4y^2+10x^2+12xy+6x+7=\left(4y^2+12xy+9x^2\right)+x^2+6x+9-2=\left(2y+3x\right)^2+\left(x+3\right)^2-2\ge-2\)

d) \(3-10x^2-4xy-4y^2=3-\left(4y^2+4xy+x^2\right)-9x^2=-\left(2y+x\right)^2-9x^2+3\le3\)

e)\(x^2-5x+y^2-xy-4y+16=\left(\frac{1}{2}x^2-xy+\frac{1}{2}y^2\right)+\frac{1}{2}\left(x^2-10x+25\right)+\frac{1}{2}\left(y^2-8y+16\right)-\frac{9}{2}=\frac{1}{2}\left(x-y\right)^2+\frac{1}{2}\left(x-5\right)^2+\frac{1}{2}\left(y-4\right)^2-\frac{9}{2}\ge-\frac{9}{2}\)Phần e) mới nghĩ đk v, tui biết đáp án sao do k xảy ra dấu bằng

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

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

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 ^_^

a) x² + x + \(\frac{1}{4}\) = ( x + \(\frac{1}{2}\) )²

b) x² + 12xy + 36xy² = ( x + y)²

c) 4x² - 12xy + 9y² = ( 2x - 3y)²

d) x² - 2x + 4 = ( x - 2)²

e) 25x² + 4y² - 20xy = ( 5x - 2y)²

bình phương tổng chứ

b, B= x^2+ 2xy+y^2 +4y+4

= x^2+2xy+y^2+y^2+4y+4

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

c, C= 2x^2+6xy+9y^2+2x+1

= x^2+6xy+9y^2+x^2+2x+1

= (x+3)^2+(x+1)^2

d, D= x(x+2) +(x+1)(x+3) +2

= x^2+2x+x^2+3x+x+3+2

= x^2+2x+1+x^2+4x+4

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

e, E= x^2-2xy+2y^2+2y+1

= x^2-2xy+y^2+y^2+2y+1

= (x-y)^2+(y+1)^2

f, F= 4x^2-12xy+10y^2+4y+4

=4x^2-12xy+9y^2+y^2+4y+4

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

g, G=2x^2+4xy+4y^2+4x+4

=x^2+4xy+4y^2+x^2+4x+4

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

Xong r.... dài quá...mới hè lớp 7 nên có j bỏ qua ak

giúp mình vs ạ

Câu a đề có sai ko bn

a. \(9x^2+25-12xy+5y^2-10y\)

\(=\left(9x^2-12xy+4y^2\right)+\left(25+y^2-10y\right)\)

\(=9\left(x^2-\frac{4xy}{3}+\frac{4y^2}{9}\right)+\left(5-y\right)^2\)

\(=9\left(x-\frac{2y}{3}\right)^2+\left(5-y\right)^2\)

a) \(4x^2-4xy+y^2-9\)

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

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

b) \(x^2-36+4xy+4y^2\)

\(=\left(4y^2+4xy+x^2\right)-36\)

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

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

c) \(9x^2-12xy-25+4y^2\)

\(=\left(9x^2-12xy+4y^2\right)-25\)

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

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

d) \(25x^2+10x-4y^2+1\)

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

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

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

a)\(6x-9-x^2\)

\(=-\left(x^2+6x+9\right)\)

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

b)\(x^2+4y^2+4xy\)

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

c)\(x^2+8x+16\)

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

d)\(9x^2-12xy+4y^2\)

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

e)\(-25x^2y^2+10xy-1\)

\(=-\left(25x^2y^2-10xy+1\right)\)

\(=-\left(5xy-1\right)^2\)

f)\(4x^2-4x+1\)

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

j)\(x^2+6x+9\)

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

h)\(9x^2-6x+1\)

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

#H

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

b, x² + 4y² + 4xy = x² + 2. x . 2y + (2y)² = (x + 2y)²

c, x² + 8x + 16 = x² + 2 . x . 4 + 4² = (x + 4)²

d, 9x² - 12xy + 4y² = (3x)² - 2 . 3x . 2y + (2y)² = (3x - 2y)²

e, - 25x²y² + 10xy - 1 = - (25x²y² - 10xy + 1) = - [(5xy)² - 2 . 5xy + 1] = - (5xy - 1)²

f, 4x² - 4x + 1 = (2x)² - 2 . 2x + 1 = (2x - 1)²

j, x² + 6x + 9 = x² + 2 . x . 3 + 3² = (x + 3)²

h, 9x² - 6x + 1 = (3x)² - 2 . 3x + 1 = (3x - 1)²