Câu 21: 

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

Câu 22:

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

\(a,=\left(3+x\right)\left(9-3x+x^2\right)\\ b,=\left(4x+0,1\right)\left(16x^2-0,4x+0,01\right)\\ c,=\left(2-3x\right)\left(4+6x+9x^2\right)\\ d,=\left(\dfrac{x}{5}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{25}+\dfrac{xy}{15}+\dfrac{y^2}{9}\right)\)

a) \(27+x^3=3^3+x^3=\left(3+x\right)\left(9-3x+x^2\right)\)

b) \(64x^3+0,001=\left(4x\right)^3+\left(\dfrac{1}{10}\right)^3=\left(4x+\dfrac{1}{10}\right)\left(16x^2-\dfrac{4x}{10}+\dfrac{1}{100}\right)\)

a/\(27+x^3=\left(3+x\right)\left(9-3x+x^2\right)\)

b/ \(64x^3+0,001=\left(4x+0,1\right)\left(16x^2-0,4x+0,01\right)\)

c/ \(8-27x^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)

d/ \(\dfrac{x^3}{125}-\dfrac{y^3}{27}=\left(\dfrac{x}{5}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{25}+\dfrac{xy}{15}+\dfrac{y^2}{9}\right)\)

`a, (2x+3)^2 = 4x^2 + 12x + 9`

`b, (3x-2)^3 = 27x^3  - 54x^2 + 36x - 8`

2:

-8x^6-12x^4y-6x^2y^2-y^3

=-(8x^6+12x^4y+6x^2y^2+y^3)

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

3:

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

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

Đề bài không chính xác, biểu thức này không viết được dưới dạnh tích

a: \(x^3+\left(2y\right)^3=\left(x+2y\right)\left[x^2-x\cdot2y+\left(2y\right)^2\right]\)

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

b: \(\left(2x\right)^3-y^3\)

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

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

\(a,(x^3-x+1)(2x+1)+(x-1)(x+2)\)

\(=2x^4-2x^2+2x+x^3-x+1+x^2-x+2x-2\)

\(=2x^4+x^3+(-2x^2+x^2)+(2x-x-x+2x)+(1-2)\)

\(=2x^4+x^3-x^2+2x-1\)

\(b,(2x+a)(2x-3a)-5a(x+3)\)

\(=4x^2+2ax-6ax-3a^2-5ax-15a\)

\(=4x^2+(2ax-6ax-5ax)-3a^2-15a\)

\(=4x^2-9ax-3a^2-15a\)

Chúc bạn học tốt

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

\(=2x^4+x^3-2x^2-x+2x+1+x^2+2x-x-2\)

\(=2x^4+x^3-x^2+2x-1\)

b, \(\left(2x+a\right)\left(2x-3a\right)-5a\left(x+3\right)\)

\(=4x^2-6xa+2ax-3a^2-5ax-15a\)

\(=4x^2-9ax-3a^2-15a\)

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

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

\(=2x^4-2x^2+2x+x^3-x+1+x^2+2x-x-2\)

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

\(=2x^4-x^2+2x+x^3-1\)

b,\(\left(2x+a\right)\left(2x-3a\right)-5a\left(x+3\right)\)

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

\(=4x^2-6ax+2ax-3a^2-5ax-15a\)

\(=4x^2+\left(-6ax+2ax-5ax\right)-3a^2-15a\)

\(=4x^2-9ax-3a^2-15a\)

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/ (3x+a)(2x-5a)-6a(2x-a)

=6x\(^2\)-15ax+2ax-5a\(^2\)-12ax+6a\(^2\)

=6x\(^2\)+a\(^2\)-25ax