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

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

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

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

ghytyyj

Trả lời:

7, 49y² - x² + 6x - 9

= 49y² - ( x² - 6x + 9 )

 = ( 7y )² - ( x - 3 )²

= ( 7y - x + 3 ) ( 7y - x - 3 )

8, sửa đề: 25x² - 4y² - 4y - 1

= 25x² - ( 4y² + 4y + 1 )

= ( 5x )² - ( 2y + 1 )

= ( 5x - 2y - 1 ) ( 5x + 2y + 1 )

9, 4x² - y² + 8y - 16

= 4x² - ( y² - 8y + 16 )

= ( 2x )² - ( y - 4 )²

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

a, \(49y^2-x^2+6x-9=49y^2-\left(x-3\right)^2=\left(7y-x+3\right)\left(7y+x-3\right)\)

b, đề sai rồi bạn 

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

(2x +y-4)

\(1,x^2-y^2+4x-4y\)

\(\left(x-y\right)\left(x+y\right)+4\left(x-y\right)\)

\(\left(x-y\right)\left(x+y+4\right)\)

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

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

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

\(3,3x^2-4y+4x-3y^2\)

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

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

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

\(x^4-6x^3+54x-81\)

\(x^4+3x^3-9x^3+27x^2-27x^2+81x-27x-81\)

\(\left(x^4+3x^3\right)-\left(9x^3+27x^2\right)+\left(27x^2+81x\right)-\left(27x+81\right)\)

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

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

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

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 )

Trả lời:

5, x² - y² + 4x + 4 

= ( x² + 4x + 4 ) - y²

= ( x + 2 )² - y²

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

6, x² + 2x - 4y² - 4y

= ( x² - 4y² ) + ( 2x - 4y )

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

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

7, 3x² - 4y + 4x - 3y²

= ( 3x² - 3y² ) + ( 4x - 4y )

= 3 ( x² - y² ) + 4 ( x - y )

= 3 ( x - y ) ( x + y ) + 4 ( x - y )

= ( x - y ) [ 3 ( x + y ) + 4 ]

= ( x - y ) ( 3x + 3y + 4 )

8, x⁴ - 6x³ + 54x - 81

= ( x⁴ - 81 ) - ( 6x³ - 54x )

= ( x² - 9 ) ( x² + 9 ) - 6x ( x² - 9 )

= ( x² - 9 ) ( x² + 9 - 6x )

= ( x - 3 ) ( x + 3 ) ( x - 3 )²

= ( x - 3 )³ ( x + 3 )

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

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

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

d, \(x^4-6x^3+54x-81=\left(x^2+9\right)\left(x-3\right)\left(x+3\right)-6x\left(x^2-9\right)\)

\(=\left(x-3\right)\left(x+3\right)\left(x^2-6x+9\right)=\left(x-3\right)^3\left(x+3\right)\)

5, x²-y²+4x+4

=(x²+4x+4)-y²

=(x+2)²-y²

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

6, x²+2x-4y²-4y

=(x²-4y²)+(2x-4y)

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

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

7, 3x²-4y+4x-3y²

=(3x²-3y²)+(4x-4y)

=3(x²-y²)+4(x-y)

=3(x-y)(x+y)+4(x-y)

=(x-y)[3(x+y)+4]

=(x-y)(3x+3y+4)

8, x⁴-6x³+54x-81

=(x⁴-81)-(6x³-54x)

=(x²-9)(x²+9)-6x(x²-9)

=(x²-9)(x²+9-6x)

=(x+3)(x-3)(x-3)²

=(x+3)(x-3)³

#H