1) \(x^2-4xy+4y^2+xz-2yz\)

\(=\left(x^2-4xy+4y^2\right)+\left(xz-2yz\right)\)

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

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

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

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

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

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

a)\(6x-9-x^2\)

\(=-\left(x^2+6x+9\right)\)

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

b)\(x^2+4y^2+4xy\)

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

c)\(x^2+8x+16\)

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

d)\(9x^2-12xy+4y^2\)

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

e)\(-25x^2y^2+10xy-1\)

\(=-\left(25x^2y^2-10xy+1\right)\)

\(=-\left(5xy-1\right)^2\)

f)\(4x^2-4x+1\)

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

j)\(x^2+6x+9\)

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

h)\(9x^2-6x+1\)

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

#H

a, 6x - 9 - x² = - x² + 6x - 9 = - (x² - 6x + 9) = - (x - 3)²

b, x² + 4y² + 4xy = x² + 2. x . 2y + (2y)² = (x + 2y)²

c, x² + 8x + 16 = x² + 2 . x . 4 + 4² = (x + 4)²

d, 9x² - 12xy + 4y² = (3x)² - 2 . 3x . 2y + (2y)² = (3x - 2y)²

e, - 25x²y² + 10xy - 1 = - (25x²y² - 10xy + 1) = - [(5xy)² - 2 . 5xy + 1] = - (5xy - 1)²

f, 4x² - 4x + 1 = (2x)² - 2 . 2x + 1 = (2x - 1)²

j, x² + 6x + 9 = x² + 2 . x . 3 + 3² = (x + 3)²

h, 9x² - 6x + 1 = (3x)² - 2 . 3x + 1 = (3x - 1)²

1 x mũ 2 + 4xy + 4y mũ 2 = x^2 + 4xy + 4y^2 =(2y+x)^2

2,       4x mũ 2 - 36y mũ 2 =4x^2 -36y^2 = -4 (3y-x) (3y+x)

1, \(x^2+4xy+4y^2=\left(x+2y\right)^2\)

2, \(4x^2-36y^2=\left(2x-6y\right)\left(2x+6y\right)\)

3, \(x^3-2x^2+5x-10=x^2\left(x-2\right)+5\left(x-2\right)=\left(x^2+5\right)\left(x-2\right)\)

4, \(a^3+a^2+3a+3=a^2\left(a+1\right)+3\left(a+1\right)=\left(a^2+3\right)\left(a+1\right)\)

5, \(7x^3-21x^2+3-x=7x^2\left(x-3\right)-\left(x-3\right)=\left(7x^2-1\right)\left(x-3\right)\)

\(a,x^2+4x-y^2+4\)

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

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

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

\(b,25-4x^2-4xy-y^2\)

\(=25-\left(4x^2+4xy+y^2\right)\)

\(=5^2-\left(2x+y\right)^2\)

\(=\left(5-2x+y\right)\left(5+2x+y\right)\)

\(c,x^3-x+y^3-y\)

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

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

\(a)x^5+x^4+1\)

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

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

\(b)x^8+x^7+1\)

\(=\left(x^8-x^2\right)+\left(x^7-x\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)

\(#Tuyết\)

7,      4x mũ 2 - 12x + 9 - y mũ 2 =  -(y-2x+3) (y+2x-3)

8,      16x mũ 2 - 4y mũ 2 + 4y - 1 =   -(2y - 4x - 1) (2y+4x-1)

9,        25 - x mũ 2 - 12x - 36 =  -(x+1) (x+11)

10,        x mũ 2 - 9 - 5 ( x + 3 ) =  (x-8) (x+3)

bạn k cho mình nha 

chúc bạn học tốt :))))

bạn kham khảo link, mình đã làm rồi nhé

Câu hỏi của Phạm Đỗ Bảo Ngọc - Toán lớp 8 - Học trực tuyến OLM 

Trả lời:

7, 4x² - 12x + 9 - y²

= ( 4x² - 12x + 9 ) - y² 

= ( 2x - 3 )² - y² 

= ( 2x - 3 - y )( 2x - 3 + y )

8, 16x² - 4y² + 4y - 1

= 16x² - ( 4y² - 4y + 1 )

= ( 4x )² - ( 2y - 1 )²

= ( 4x - 2y + 1 )( 4x + 2y - 1 )

9, 25 - x² - 12x - 36

= 25 - ( x² + 12x + 36 )

= 5² - ( x + 6 )²

= ( 5 - x - 6 )( 5 + x + 6 )

= ( - 1 - x )( 11 + x )

10, x² - 9 - 5 ( x + 3 )

= ( x - 3 )( x + 3 ) - 5 ( x + 3 )

= ( x + 3 )( x - 3 - 5 )

= ( x + 3 )( x - 8 )

6, \(x^2-1+2xy+y^2=\left(x+y\right)^2-1=\left(x+y-1\right)\left(x+y+1\right)\)

7, \(4x^2-12x+9-y^2=\left(2x-3\right)^2-y^2=\left(2x-3-y\right)\left(2x-3+y\right)\)

8, \(16x^2-4y^2+4y-1=16x^2-\left(2y-1\right)^2=\left(4x-2y+1\right)\left(4x+2y-1\right)\)

9, \(25-x^2-12x-36=25-\left(x+6\right)^2=\left(5-x-6\right)\left(5+x+5\right)=-\left(x+1\right)\left(x+10\right)\)

10, \(x^2-9-5\left(x+3\right)=\left(x-3\right)\left(x+3\right)-5\left(x+3\right)=\left(x+3\right)\left(x-8\right)\)

\(a,=2xy\left(2y-x\right)\\ b,=x^2\left(x-4\right)+5\left(x-4\right)=\left(x^2+5\right)\left(x-4\right)\\ c,=\left(x-y\right)\left(x^2-25\right)=\left(x-y\right)\left(x-5\right)\left(x+5\right)\)

ghytyyj