B1: 

a) \(\left(x-4\right)\left(x+4\right)=x^2-16\)

b) \(\left(x-5\right)\left(x+5\right)=x^2-25\)

B2:

a) \(x^2-2x+1=\left(x-1\right)^2\)

b) \(x^2+2x+1=\left(x+1\right)^2\)

c) \(x^2-6x+9=\left(x-3\right)^2\)

Bài 1 :

a) \(\left(x-4\right)\left(x+4\right)=x^2-4x+4-16=x^2-16\)

b) \(\left(x-5\right)\left(x+5\right)=x^2-5x+5x-25=x^2-25\)

Bài 2 :

a) \(x^2+2x+1=x^2-x-x+1\)

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

b) \(x^2+2x+1=x^2+x+x+1\)

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

c) \(x^2-6x+9=x^2-3x-3x+9\)

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

Bài 1 : 

\(\left(x-4\right)\left(x+4\right)=x^2+4x-4x-16=x^2-16\)

\(\left(x-5\right)\left(x+5\right)=x^2+5x-5x-25=x^2-25\)

Bài 2 : 

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

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

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

\(x^2-x+\frac{1}{4}\)

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

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

=x^2+2.x.1/2+1/4= (x+1/2)^2

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

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

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

x^2+x+1/4

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

=(x+1/2)

x 2  + x + 1/4 =  x 2  + 2.x.1/2 +  1 / 2 2  =  x + 1 / 2 2

a. (x + y)² = x² + 2xy + y²

b. (x - 2y)² = x² - 4xy - 4x²

c. (xy² + 1)(xy² - 1) = x²y⁴ - 1

d. (x + y)²(x - y)² = (x² + 2xy + y²)(x² - 2xy + y²) = x⁴ - (2xy + y²)² = x⁴ - (4x²y² + y⁴) = x⁴ - 4x²y² - y⁴

^{Chucs hocj toots}

Câu 2: 

a: \(x^2-4x+4=\left(x-2\right)^2\)

b: \(x^2+10x+25=\left(x+5\right)^2\)

d: \(9\left(x+1\right)^2-6\left(x+1\right)+1=\left(3x+2\right)^2\)

e: \(\left(x-2y\right)^2-8\left(x-2xy\right)+16x^2=\left(x-2y+4x\right)^2=\left(5x-2y\right)^2\)

Câu 7:

a: Ta có: \(A=x^2-2x+7\)

\(=x^2-2x+1+6\)

\(=\left(x-1\right)^2+6\ge6\forall x\)

Dấu '=' xảy ra khi x=1

b: Ta có: \(B=5x^2-20x\)

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

\(=5\left(x-2\right)^2-20\ge-20\forall x\)

Dấu '=' xảy ra khi x=2

\(x^2+2\left(x+1\right)^2+3\left(x-2\right)^2+4\left(x+3\right)^2\)

\(=x^2+2\left(x^2+2x+1\right)+3\left(x^2-4x+4\right)+4\left(x^2+6x+9\right)\)

\(=x^2+2x^2+4x+2+3x^2-12x+12+4x^2+24x+36\)

\(=10x^2+16x+50\)

A=x^2+2(x^2+2x+1)+3(x^2+4x+4)+4(x^2+6x+9)

  =x^2+2x^2+4x+2+3x^2+12x+12+4x^2+24x+36

  =10x^2+40x+50

  =(9x^2+30x+25)+(x^2+10x+25)

  =(3x+5)^2+(x+5)^2

a. $x^2+4x+4$

$=x^2+2\cdot x\cdot2+2^2$

$=(x+2)^2$

b. $x^2-6xy+9y^2$

$=x^2-2\cdot x\cdot3y+(3y)^2$

$=(x-3y)^2$

c. $4x^2+12x+9$

$=(2x)^2+2\cdot2x\cdot3+3^2$

$=(2x+3)^2$

d. $x^2-x+\dfrac14$

$=x^2-2\cdot x\cdot \dfrac12+\Bigg(\dfrac12\Bigg)^2$

$=\Bigg(x-\dfrac12\Bigg)^2$

`x^2 +4x+4`

`=x^2+2*x*2+2^2`

`=(x+2)^2`

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`x^2-6xy+9y^2`

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

`=(x-3y)^2`

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`4x^2 +12x+9`

`=(2x)^2 +2*2x*3+3^2`

`=(2x+3)^2`

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`x^2-x+1/4`

`=x^2 - 2*x*1/2 +(1/2)^2`

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