a, a²+b²+2ab+2a+2b+1=(a+b+1)²

b,3x(x-2y)+6y(2y-x)=3x(x-2y)-6y(x-2y)

=3(x-2y)(x-2y)=3(x-2y)²

c, 16xy +4y²-9 +16x²=(16x²+16xy+4y²)-3²

=(4x-2y)²-3²=(4x-2y+3)(4x-2y-3)

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

Phương trình thuần nhất đẳng cấp bậc 8 bạn nha :D

B1 :

a, B = (x+1)^2+(y-2)^2 = (99+1)^2+(102-2)^2 =  100^2+100^2 = 20000

b, = (2x^2+16x+32)-2y^2

   = 2.(x+4)^2-2y^2

   = 2.[(x+4)^2-y^2] = 2.(x+4-y).(x+4+y)

c, <=> (x^2-3x)+(2x-6) = 0

<=> (x-3).(x+2) = 0

<=> x-3=0 hoặc x+2=0

<=> x=3 hoặc x=-2

B2 :

P = (3-x).(x+3)/x.(x-3) = -(x+3)/x = -x-3/x

k mk nha

Bai 1

a)B=(x+1)²+(y-2)²

     Voi x=99,y=102

=>B= 100²+100²

       =20000

b)\(2x^2-2y^2+16x+32\)

=\(2\left[\left(x^2+8x+16\right)-y^2\right]\)

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

=2(x-y+4)(x+y+4)

c)\(x^2-3x+2x-6=0\)

=>x(x-3)+2(x-3)=0

=>(x-3)(x+2)=0

=>x=-2;3

Bai 2

\(P=\frac{9-x^2}{x^2-3x}\)

    =\(-\frac{x^2-9}{x\left(x-3\right)}\)

   =\(-\frac{\left(x-3\right)\left(x+3\right)}{x\left(x-3\right)}\)

=\(\frac{-x-3}{x}\)

bafi 1: a) \(B=x^2+2x+1+y^2-4y+4\)

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

khi \(x=99\); \(y=102\)ta co:

\(B=\left(99+1\right)^2+\left(102-2\right)^2\)

\(B=100^2+100^2\)

\(B=10000+10000\)

\(B=20000\)

c) \(x^2-3x+2x-6=0\)

\(x\left(x-3\right)+2\left(x-3\right)=0\)

\(\left(x+2\right)\left(x-3\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+2=0\\x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)

vay \(\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)

bai 2:

\(P=\frac{9-x^2}{x^2-3x}\)

\(P=\frac{\left(3-x\right)\left(x+3\right)}{x\left(x-3\right)}\)

\(P=\frac{-\left(x+3\right)}{x}\)\(\left(x\ne0\right)\)

\(P=\frac{-x-3}{x}\)

vay \(P=\frac{-x-3}{x}\)

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

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

a) -y² + 2xy - x² + 3x - 3y

= (3x - 3y) - (x² - 2xy + y²)

= 3(x - y) - (x - y)²

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

b) x³ - 2x² - x + 2

= (x³ - x) - (2x² - 2)

= x(x² - 1) - 2(x² - 1)

= (x² - 1)(x - 2)

= (x - 2)(x - 1)(x + 1)

c) x²(x + 1) - 2x(x + 1) + x + 1

= (x + 1)(x² - 2x + 1)

= (x + 1)(x - 1)²

d) a² + b² + 2a - 2b - 2ab

= (a² - 2ab + b²) + (2a - 2b)

= (a - b)² + 2(a - b)

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

e) 4x² - 8x + 3

= (4x² - 2x) - (6x - 3)

= 2x(2x - 1) - 3(2x - 1)

= (2x - 1)(2x - 3)

f) 25 - 16x²

= 5² - (4x)²

= (5 - 4x)(5 + 4x)

a, -y² + 2xy - x² + 3x - 3y

= - (x² - 2xy + y²) + 3(x - y)

= - (x - y)² + 3(x - y)

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

b, x³ - 2x² - x + 2

= x² (x - 2) - (x - 2)

= (x - 2)(x² - 1)

= (x - 2)(x - 1)(x + 1)

c, x² (x + 1) - 2x(x + 1) + x + 1

= x² (x + 1) - 2x(x + 1) + (x + 1)

= (x + 1)(x² - 2x + 1)

= (x + 1)(x - 1)²

d, a² + b² + 2a - 2b - 2ab

= (a² - 2ab + b² )+ (2a - 2b)

= (a - b)² + 2(a - b)

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

e, 4x² - 8x + 3

= 4x² - 2x - 6x + 3

= 2x( 2x - 1) - 3(2x - 1)

= (2x - 1)(2x - 3)

f, 25 - 16x²

= 5² - (4x)²

= (5 - 4x)(5 + 4x)

Chúc bạn học tốt!

a) \(\frac{1}{4}x^2-5xy+25y^2=\left(\frac{1}{2}x\right)^2-5xy+\left(5y\right)^2\)

\(=\left(\frac{1}{2}x-5y\right)^2\)

b) \(\left(7x-4\right)^2-\left(2x+1\right)^2\)

\(=\left(7x-4+2x+1\right)\times\left(7x-4-2x-1\right)=\left(9x-3\right)\times\left(5x-5\right)\)

\(=3\times5\times\left(3x-1\right)\times\left(x-1\right)=15\times\left(3x-1\right)\times\left(x-1\right)\)

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

d) \(125-x^6=5^3-\left(x^2\right)^3=\left(5-x^2\right)\left(25+5x^2+x^4\right)\)

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

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

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

a, bậc 6 

b, bậc 6 

c, bậc 12 

d, bậc 9 

e, bậc 8