a) M = 8ab;

b) N = [ ( 3 a   + +   2 )   +   ( 1   –   2 b ) ] 2   =   ( 3 a   –   2 b   +   3 ) 2 .

Bài 2:

a) \(\left(x+5\right)^2=x^2+10x+25\)

b) \(\left(\dfrac{5}{2}-t\right)^2=\dfrac{25}{4}-5t+t^2\)

c) \(\left(2u+3v\right)^2=4u^2+12uv+9v^2\)

d) \(\left(-\dfrac{1}{8}a+\dfrac{2}{3}bc\right)^2=\dfrac{1}{64}a^2-\dfrac{1}{6}abc+\dfrac{4}{9}b^2c^2\)

e) \(\left(\dfrac{x}{y}-\dfrac{1}{z}\right)^2=\dfrac{x^2}{y^2}-\dfrac{2x}{yz}+\dfrac{1}{z^2}\)

f) \(\left(\dfrac{mn}{4}-\dfrac{x}{6}\right)\left(\dfrac{mn}{4}+\dfrac{x}{6}\right)=\dfrac{m^2n^2}{16}-\dfrac{x^2}{36}\)

Bài 1:

$M=(2a+b)^2-(b-2a)^2=[(2a+b)-(b-2a)][(2a+b)+(b-2a)]$

$=4a.2b=8ab$

$N=(3a+1)^2+2a(1-2b)+(2b-1)^2$

$=(9a^2+6a+1)+2a-4ab+(4b^2-4b+1)$
$=9a^2+8a+4b^2-4b-4ab+2$

$A=(m-n)^2+4mn=m^2-2mn+n^2+4mn$

$=m^2+2mn+n^2=(m+n)^2$

Bài 1: 

a: Ta có: \(M=\left(2a+b\right)^2-\left(b-2a\right)^2\)

\(=4a^2+4ab+b^2-b^2+4ab-4a^2\)

\(=8ab\)

b: Ta có: \(N=\left(3a+2\right)^2+2a\left(1-2b\right)+\left(2b-1\right)^2\)

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

\(=\left(3a-2b+3\right)^2\)

\(=9a^2+4b^2+9-12ab+18a-12b\)

c: Ta có: \(A=\left(m-n\right)^2+4nm\)

\(=m^2-2mn+n^2+4mn\)

\(=m^2+2mn+n^2\)

\(=\left(m+n\right)^2\)

2: 

a: \(\left(x+5\right)^2=x^2+10x+25\)

b: \(\left(\dfrac{5}{2}-t\right)^2=\dfrac{25}{4}-5t+t^2\)

a) \(=6a-3+15-5a=a+12\)

b) \(=25x-12x+4+35-14x=-x+39\)

d) \(=2ab+8a^2-b^2-4ab+2ab-6a^2=2a^2-b^2\)

e) \(=x+x^2-x^3+x^4-x^5+1+x-x^2+x^3-x^4=-x^5+2x+1\)

f) \(=6y^3-3y^2+y-y+y^2-y^3-y^2+y=5y^3-3y^2+y\)

a) 3( 2a -1) +5( 3-a)

   = 3. 2a -3.1 +5. 3- 5.a

   = 6a -3+ 15-5a

   =(6a -5a )+ (-3+ 15)

b) 25x - 4(3x - 1) +7(5 - 2x)

   = 25x -4.3x + 4.1 + 7.5 - 7.2

   =25x - 12x + 4 +35 - 14x

   = (25x-12x-14x)+(4+35)

   = -x=39

c) -12x3 -x1-2x-18x2

   = -36x-x-2x-36x

   = -75x

d) (2a-b)(b+4a)+2a(b-3a)

   = 2ab+2a4a-bb-b4a+2ab-2a3b

   = 2ab+8a²-b²-4ab+2ab-6a²

   =(2ab-4ab+2ab)+(8a²-6a²)-b²

   = 2a²-b²

e) (x+1)(2+x-x2+x3-x4)

   = (x+1)(2-2x)

   = x2-x2x+1.2-1.2x

   =(2x-2x)-2x²+2

   = -2x²+2

\(\dfrac{a^2b^2}{2a^2+b^2+3a^2b^2}=\dfrac{a^2b^2}{\left(a^2+b^2\right)+\left(a^2+a^2b^2\right)+2a^2b^2}\le\dfrac{a^2b^2}{2ab+2a^2b+2a^2b^2}=\dfrac{ab}{2\left(1+a+ab\right)}\)

Tương tự và cộng lại;

\(P\le\dfrac{1}{2}\left(\dfrac{ab}{1+a+ab}+\dfrac{bc}{1+b+bc}+\dfrac{ca}{1+c+ca}\right)\)

\(P\le\dfrac{1}{2}\left(\dfrac{ab}{1+a+ab}+\dfrac{abc}{a+ab+abc}+\dfrac{ab.ca}{ab+abc+ab.ca}\right)\)

\(P\le\dfrac{1}{2}\left(\dfrac{ab}{1+a+ab}+\dfrac{1}{a+ab+1}+\dfrac{a}{ab+1+a}\right)=\dfrac{1}{2}\)

Dấu "=" xảy ra khi \(a=b=c=1\)

a) Ta có: \(A=\dfrac{a^2-1}{3}\cdot\sqrt{\dfrac{9}{\left(1-a\right)^2}}\)

\(=\dfrac{\left(a+1\right)\cdot\left(a-1\right)}{3}\cdot\dfrac{3}{\left|1-a\right|}\)

\(=\dfrac{\left(a+1\right)\left(a-1\right)}{1-a}\)

=-a-1

b) Ta có: \(B=\sqrt{\left(3a-5\right)^2}-2a+4\)

\(=\left|3a-5\right|-2a+4\)

\(=5-3a-2a+4\)

=9-5a

c) Ta có: \(C=4a-3-\sqrt{\left(2a-1\right)^2}\)

\(=4a-3-\left|2a-1\right|\)

\(=4a-3-2a+1\)

\(=2a-2\)

d) Ta có: \(D=\dfrac{a-2}{4}\cdot\sqrt{\dfrac{16a^4}{\left(a-2\right)^2}}\)

\(=\dfrac{a-2}{4}\cdot\dfrac{4a^2}{\left|a-2\right|}\)

\(=\dfrac{a^2\left(a-2\right)}{-\left(a-2\right)}\)

\(=-a^2\)

A =(a+b-2c) -(-a+b+c) -(2a-b-c)

   = a+b-2c+a-b-c-2a+b+c

   = b-2c

B=-(2a-b+c) + (b-2c-3a) -(-5a-3c+b)

  = -2a+b-c+b-2c-3a+5a+3c-b

  = b-c

C=(3a-b-2c)-( 2b+3c-a) +(2a-3b)

  = a-b-2c-2b-3c+a+2a-3b

  = -6b-5c

D=(5a-3b+c) +( 2a-3b+5) -( b-c+a)

   = 5a-3b+c+2a-3b+5-b+c-a

   = 6a-7b+2c

\(A=\left(a+b-2c\right)-\left(-a+b+c\right)-\left(2a-b-c\right)\)

\(=a+b-2c+a-b-c-2a+b+c=b-2c\)

\(B=-\left(2a-b+c\right)+\left(b-2c-3a\right)-\left(-5a-3c+b\right)\)

\(=-2a+b-c+b-2c-3a+5a+3c-b=b\)

\(C=\left(3a-b-2c\right)-\left(2b+3c-a\right)+\left(2a-3b\right)\)

\(=3a-b-2c-2b-3c+a+2a-3b=6a-6b-5c\)

\(D=\left(5a-3b+c\right)+\left(2a-3b+5\right)-\left(b-c+a\right)\)

\(=5a-3b+c+2a-3b+5-b+c-a=6a-7b+2c\)

a/  (2a+3b)^2 = (2a)^2+2.2a.3b+(3b)^2 = 4a^2+12ab+9b^2

b/   ta nhân đa thức với đa thức thì kết quả sẽ = -9a^2+25

c/   (x^2-3y)^2= (x^2)^2-2.x^2.3y+(3y)^2= x^4-6x^2y+9y^2

a) A=(4-5x)²-(3+5x)²=(4-5x-3-5x)(4-5x+3+5x)=(-25x+1)1=-25x+1

B=(3x-1)(1+3x)-(3x+1)²=9x²-1-(3x+1)²=9x²-1-(9x²+6x+1)=9x²-1-9x²-6x-1=-6x-2=-2(3x+1)