\(1,=x\left(2x+3\right)-\left(2x+3\right)=2x^2+3x-2x-3=2x^2+x-3\\ 2,=\left(2x\right)^2-2.2.x.1+1^2=4x^2-4x+1\)

1. =2x²-2x+3x-3

2. (2x)²-2.2x.1+1²

=4x²-4x+1

5:

a: (2x-5)(2x+5)=4x^2-25

b: (3x-5y)(3x+5y)=9x^2-25y^2

c: (3x+7y)(3x-7y)=9x^2-49y^2

d: (2x-1)(2x+1)=4x^2-1

4:

a: 2003*2005=(2004-1)(2004+1)=2004^2-1<2004^2

b: 8(7^2+1)(7^4+1)(7^8+1)

=1/6*(7-1)(7+1)(7^2+1)(7^4+1)(7^8+1)

=1/6(7^2-1)(7^2+1)(7^4+1)(7^8+1)

=1/6(7^16-1)<7^16-1

5:

a: (2x-5)(2x+5)=4x^2-25

b: (3x-5y)(3x+5y)=9x^2-25y^2

c: (3x+7y)(3x-7y)=9x^2-49y^2

d: (2x-1)(2x+1)=4x^2-1

mik chỉ biết bài 5 thôi !

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

Q) (2x-3) (2x+3) =(2x)^2-3^2= 4x^2-9

\(\left(5x+3yz\right)^2=25x^2+30xyz+9y^2z^2\\ \left(2x-3\right)^3=8x^3-36x^2+54x-27\)

\(\left(y^{2x}+3yz\right)^2=y^{4x}+6y^{2x+1}z+9y^2z^2\\ \left(x^2-6z\right)\left(x^2+6z\right)=x^4-36z^2\\ \left(y-5\right)\left(25+2y+y^2+3y\right)=\left(y-5\right)\left(y^2+5y+25\right)=y^3-125\)

\(4x^2-12x+9\)

(2x+3)²

a) \(\left(2x+1\right)^3\)

\(=\left(2x\right)^3+3.\left(2x\right)^2.1+3.2x.1+1\)

\(=8x^3+12x^2+6x+1\)

b) \(\left(x-3\right)^3\)

\(=x^3-3.x^2.3+3.x.3^2-3^3\)

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

Bài 2: 

a: \(x^3+15x^2+75x+125=\left(x+5\right)^3\)

b: \(1-15y+75y^2-125y^3=\left(1-5y\right)^3\)

c: \(8x^3+4x^2y+\dfrac{3}{2}xy^2+8y^3=\left(2x+2y\right)^3\)

a) \(=4x^2-12x+9\)

b) \(=4x^2+2x+\dfrac{1}{4}\)

c) \(=4x^2-\dfrac{4}{3}x+\dfrac{1}{9}\)

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

e) \(=\left(3-\dfrac{x}{2}\right)\left(9+\dfrac{3x}{2}+\dfrac{x^2}{4}\right)\)

f) \(=\left(125-4x\right)\left(125^2+500x+16x^2\right)\)

(2x-1)(2x+1)(4x² +1)

= (4x² - 1)(4x²+1)

=16x⁴ - 1 

(2x-1).(2x+1).(4x^2+1)

= (4x^2 - 1).(4x^2+1)

=  (4x^2)^2  -  1

=  16x^4  - 1

`(2x-1)(2x+1)(4x^2+1)`

`=[(2x)^2-1^2](4x^2+1)`

`=(4x^2-1)(4x^2+1)`

`=(4x^2)^2-1^2`

`=16x^4-1`

a)
x³+3x²+3x+1
b)8x³+18x²+54x+27
c)x³+3636x²+3636x+1780360128
d)x⁶-6x²+12x-8
e)
8x³-36x²y+54xy²-27y³