\(x^2\) + 4\(x\) + 6\(xy\) + 12y + 9y\(^2\) + 4

= (\(x^2\) + 3\(xy\)) + (3\(xy\) + 9y\(^2\)) + (4\(x\) + 12y) 4

= \(x\).(\(x+3y\)) + 3y(\(x\) + 3y) + 4\(\)(\(x\) + 3y) + 4

= (\(x\) + 3y)(\(x\) + 3y) + 2(\(\)\(x+3y\)) + [2(\(x\) + 3y) + 4]

= (\(x\) + 3y)(\(x+3y+2\)) + 2(\(x+3y+2\))

= (\(x+3y+2\))(\(x+3y+2\))

= (\(x+3y+2\))\(^2\) (đpcm)

Câu 21: 

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

Câu 22:

\(x^2-8x+16=\left(x-4\right)^2\)

a) \(A=8x^3+12x^2y+6xy^2+y^3=\left(2x+y\right)^3\)

b) \(B=x^3+3x^2+3x+1=\left(x+1\right)^3\)

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

d)  \(D=27+27y^2+9y^4+y^6=\left(3+y^2\right)^3\)

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`

__

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

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

`=(x-3y)^2`

__

`4x^2 +12x+9`

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

`=(2x+3)^2`

__

`x^2-x+1/4`

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

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

x^2+6xy+9y^2-3x-9y+2

=( x^2+6xy+9y^2)-3(x+3y)+9/4 -1/4

=(x+3y)^2-3(x+3y)+(3/2)^2- 1/4

=(x+3y+3/2)^2-(1/2)^2

=(x+3y+3/2+1/2)(x+3y+3/2-1/2)=(x+3y+2)(x+3y+1)

\(x^2-6xy+9y^2\)

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

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

viết các đa thức sau dưới dạng bình phương của một tổng hoặc hiệu 

4x² + 4x + 1 

a) \(4\left(x+y\right)\)

b) \(\left(x-3y\right)^2\)

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

a) \(4 (x + y)\)

b) \((x - 3y)^2\)

c) \(x^3 - x - x^2 + 1 = x (x^2 - 1) - (x^2 - 1) = (x^2 - 1) (x - 1) = (x - 1) (x + 1) (x - 1)\)

x²-6xy+9y²-36 =(x²-6xy+9y²)-36 =(x-3y)²-6² =(x-3y+6)(x-3y-6)