B1

a, \(=>A=\left(x+y+x-y\right)\left(x+y-x+y\right)=2x.2y=4xy\)

b, \(=>B=\left[\left(x+y\right)-\left(x-y\right)\right]^2=\left[x+y-x+y\right]^2=\left[2y\right]^2=4y^2\)

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

\(=\)\(\left(x+1\right)\left(x^2-x+1\right)\left(x-1\right)\left(x^2+x+1\right)=\left(x^3+1^3\right)\left(x^3-1^3\right)=x^6-1\)

d, \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)

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

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

\(+\left(a-b+c+b-c\right)\left(a-b+c-b+c\right)\)

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

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

B2:

\(\)\(x+y=3=>\left(x+y\right)^2=9=>x^2+2xy+y^2=9\)

\(=>xy=\dfrac{9-\left(x^2+y^2\right)}{2}=\dfrac{9-\left(17\right)}{2}=-4\)

\(=>x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=3\left(17+4\right)=63\)

Bài 1: 

a) Ta có: \(\left(x+y\right)^2-\left(x-y\right)^2\)

\(=x^2+2xy+y^2-x^2+2xy+y^2\)

=4xy

b) Ta có: \(\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)

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

\(=\left(2y\right)^2=4y^2\)

c) Ta có: \(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)

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

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

\(=x^6-1\)

d) Ta có: \(\left(a+b-c\right)^2+\left(a+b+c\right)^2-2\left(b-c\right)^2\)

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

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

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

\(=a^2+2ab-2ac+a^2-2ab+2ac-4bc\)

\(=2a^2-4bc\)

Bài 2: 

Ta có: x+y=3

nên \(\left(x+y\right)^2=9\)

\(\Leftrightarrow2xy+17=9\)

\(\Leftrightarrow2xy=-8\)

hay xy=-4

Ta có: \(x^3+y^3\)

\(=\left(x+y\right)^3-3xy\left(x+y\right)\)

\(=3^3-3\cdot\left(-4\right)\cdot3\)

\(=27+36=63\)

a: Ta có: \(\left(x^2+x-1\right)^2-\left(x^2+2x+3\right)^2\)

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

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

b: Ta có: \(\left(x-3\right)^2-16\)

\(=\left(x-3-4\right)\left(x-3+4\right)\)

\(=\left(x+1\right)\left(x-7\right)\)

c: \(y^2+16y+64=\left(y+8\right)^2\)

Bài 1: 

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

Bài 2: 

a: \(4x^2+4x+1\)

b: \(9x^2+9x+\dfrac{9}{4}\)

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 !

Bài 9:

a) Ta có: \(A=\left(2x+y\right)^2-\left(2x+y\right)\left(2x-y\right)+y\left(x-y\right)\)

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

\(=3xy-y^2\)

\(=3\cdot\left(-2\right)\cdot3-3^2=-18-9=-27\)

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

\(=a^2-6ab+9b^2-a^2-6ab-9b^2-ab+2a+b-2\)

\(=-13ab+2a+b-2\)

\(=-13\cdot\dfrac{1}{2}\cdot\left(-3\right)+2\cdot\dfrac{1}{2}+\left(-3\right)-2\)

\(=\dfrac{31}{2}\)

Bài 7: 

a) \(498^2=\left(500-2\right)^2=250000-2000+4=248004\)

b) \(93\cdot107=100^2-7^2=10000-49=9951\)

c) \(163^2+74\cdot163+37^2=\left(163+37\right)^2=200^2=40000\)

d) \(1995^2-1994\cdot1996=1995^2-1995^2+1=1\)

e) \(9^8\cdot2^8-\left(18^4-1\right)\left(18^4+1\right)\)

\(=18^8-18^8+1=1\)

f) \(125^2-2\cdot125\cdot25+25^2=\left(125-25\right)^2=100^2=10000\)

Bài 8:

a) Ta có: \(\left(x^2+3x+1\right)^2-2\left(x^2+3x+1\right)\left(3x-1\right)+\left(3x-1\right)^2\)

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

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

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

b) Ta có: \(\left(3x^3+3x+1\right)\left(3x^3-3x+1\right)-\left(3x^3+1\right)^2\)

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

\(=-9x^2\)

c) Ta có: \(\left(2x^2+2x+1\right)\left(2x^2-2x+1\right)-\left(2x^2+1\right)^2\)

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

\(=-4x^2\)

a. (3a + 1)³

= 27a³ + 27a² + 9a + 1

a. \(\left(3b+\dfrac{5a}{6}\right)^2\)

= \(9b^2+15ab+\dfrac{25a^2}{36}\)

b. (5x - y)²

= 25x² - 10xy + y²

c. (2a + b - 5)(2a - b + 5)

= 4a² - (b - 5)²

d. \(\left(x^2+\dfrac{2}{5y}\right)\left(x^2-\dfrac{2}{5y}\right)\)

= \(x^4-\dfrac{4}{25y^2}\)