\(\left(1-3x\right)^3=1-9x+27x^2-27x^3\)

\(\left(2-3x\right)^3=8-36x+54x^2-27x^3\)

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

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 !

a) $(3x+5)^2\\=(3x)^2+2.3x.5+5^2\\=9x^2+30x+25$

b) $(6x+\dfrac{1}{3})^2\\=(6x)^2+2.6x.\dfrac{1}{3}+(\dfrac{1}{3})^2\\=36x^2+4x+\dfrac{1}{9}$

c) $(5x-4y)^2\\=(5x)^2-2.5x.4y+(4y)^2\\=25x^2-40xy+16y^2$

d) $(5x-3)(5x+3)\\=(5x)^2-(3)^2\\=25x^2-9$

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

( A   –   B ) 3   =   ( A   +   ( - B ) ) 3       =   A 3   +   3 . A 2 . ( - B )   +   3 . A . ( - B ) 2   +   ( - B ) 3       =   A 3   –   3 A 2 B   +   3 A B 2   –   B 3     = >   ( A   –   B ) 3   =   A 3   –   3 A 2 B   –   3 A B 2   +   B 3

là sai

Đáp án cần chọn là: B

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

\(=\left(3x\right)^3-3\left(3x\right)^2\cdot2a+3\cdot3x\cdot\left(2a\right)^2-\left(2a\right)^3\)

\(=27x^3-3\cdot9x^2\cdot2a+3\cdot3x\cdot4a^2-8a^3\)

\(=27x^3-54ax^2+36a^2x-8a^3\)

2) \(\left(\dfrac{x+y}{3}\right)^3\)

\(=\dfrac{\left(x+y\right)^3}{27}\)

\(=\dfrac{x^3+3x^2y+3xy^2+y^3}{27}\)

3) \(\left(3x+\dfrac{y}{3}\right)^3\)

\(=\dfrac{\left(3x+y\right)^3}{27}\)

\(=\dfrac{27x^3+27x^2y+9xy^2+y^3}{27}\)

\(F=\left(3x-2\right)^2+\left(3x+2\right)^2+2\left(9x^2-4\right)\\=\left[\left(3x+2\right)^2+2.\left(3x+2\right)\left(3x-2\right)+\left(3x-2\right)^2\right]\\ =\left[\left(3x+2\right)+\left(3x-2\right)\right]^2\\ =\left(6x\right)^2=36x^2\\ Thay.x=-\dfrac{1}{3}.vào.F.thu.gọn:\\ F=36x^2=36.\left(-\dfrac{1}{3}\right)^2=36.\left(\dfrac{1}{9}\right)=4\)

a: \(=x^2-12x+36\)

b: \(=x^3+9x^2+27x+27\)

A.x=6

b.x=-3