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

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

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

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

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

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

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

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

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

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

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

6, x mũ 4 - 4x mũ 3 - 8x mũ 2 + 8x =x (x+2) (x^2-6x+4)

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

10, 4x mũ 2 ( x + y ) -x - y  = (2x-1) (2x+1) (y+x)

f) = x²( x - 4 ) - 9( x - 4 ) = ( x - 4 )( x - 3 )( x + 3 )

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

h) = x³( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x³ + x - 1 )

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

j) = ( x - y )( x² + xy + y² ) - 3( x - y ) = ( x - y )( x² + xy + y² - 3 )

Trả lời:

f, x³ - 4x² - 9x + 36 = ( x³ - 4x² ) - ( 9x - 36 ) = x² ( x - 4 ) - 9 ( x - 4 ) = ( x - 4 )( x² - 9 ) = ( x - 4 )( x - 3 )( x + 3 )

g, 4x - 4y + x² - 2xy + y² = ( 4x - 4y ) + ( x² - 2xy + y² ) = 4 ( x - y ) + ( x - y )² = ( x - y ) ( 4 + x - y )

h, x⁴ + x³ + x² - 1 = ( x⁴ + x³ ) + ( x² - 1 ) =  x³ ( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x³ + x - 1 ) 

i, x² - y² - 4x - 4y = ( x² - y² ) - ( 4x + 4y ) = ( x - y )( x + y ) - 4 ( x + y ) = ( x + y )( x - y - 4 )

j, x³ - y³ - 3x + 3y = ( x³ - y³ ) - ( 3x - 3y ) = ( x - y )( x² + xy + y² ) - 3 ( x - y ) = ( x - y )( x² + xy + y² - 3 ) 

f) x³-4x²-9x+36

=x²(x-4)-9(x-4)

=(x-4)(x²-9)

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

g) 4x-4y+x²-2xy+y²

=4(x-y)+(x-y)²

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

h) x⁴+x³+x²-1

=x³(x+1)+(x-1)(x+1)

=(x+1)(x³+x-1)

i) x²-y²-4x-4y

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

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

j) x³-y³-3x+3y

=(x-y)(x²+xy+y²)-3(x-y)

=(x-y)(x²+xy+y²-3)

#H

s) = ( x² - 2xy + y² ) - ( 2xy )² = ( x - y - 2xy )( x - y + 2xy )

u) sửa +4y thành -4y

= 4( x - y ) - x²( x - y ) = ( x - y )( 2 - x )( 2 + x )

Trả lời:

s, x² - 4x²y² + y² - 2xy

= ( x² - 2xy + y² ) - 4x²y²

= ( x - y )² - ( 2xy )² 

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

u, sửa đề: 4x - 4y - x² ( x - y )

= 4 ( x - y ) - x² ( x - y )

= ( x - y ) ( 4 - x² )

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

a)x²−2x−4y²−4ya)x²-2x-4y²-4y

=x²−2x−4y²−4y+2xy−2xy=x²-2x-4y²-4y+2xy-2xy

=(x²−2xy−2x)+(2xy−4y²−4y)=(x²-2xy-2x)+(2xy-4y²-4y)

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

=(x+2y)(x−2y−2)=(x+2y)(x-2y-2)

b)x4+2x³−4x−4b)x4+2x³-4x-4

=x4+2x³+2x²−2x²−4x−4=x4+2x³+2x²-2x²-4x-4

=(x4+2x³+2x²)−(2x²+4x+4)=(x4+2x³+2x²)-(2x²+4x+4)

=x²(x²+2x+2)−2(x²+2x+2)=x²(x²+2x+2)-2(x²+2x+2)

=(x²−2)(x²+2x+2)=(x²-2)(x²+2x+2)

c)x³+2x²y−x−2yc)x³+2x²y-x-2y

=x²(x+2y)−(x+2y)=x²(x+2y)-(x+2y)

=(x²−1)(x+2y)=(x²-1)(x+2y)

=(x+1)(x−1)(x+2y)=(x+1)(x-1)(x+2y)

d)3x²−3y²−2(x−y)²d)3x²-3y²-2(x-y)²

=3(x²−y²)−2(x−y)²=3(x²-y²)-2(x-y)²

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

=(x−y)[3(x+y)−2(x−y)]=(x-y)[3(x+y)-2(x-y)]

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

=(x−y)(x+5y)=(x-y)(x+5y)

e)x³−4x²−9x+36e)x³-4x²-9x+36

=(x³−4x²)−(9x−36)=(x³-4x²)-(9x-36)

=x²(x−4)−9(x−4)=x²(x-4)-9(x-4)

=(x−4)(x²−9)=(x-4)(x²-9)

=(x−4)(x²−3²)=(x-4)(x²-3²)

=(x−4)(x+3)(x−3)=(x-4)(x+3)(x-3)

f)x²−y²−2x−2yf)x²-y²-2x-2y

=(x²−y²)−(2x+2y)=(x²-y²)-(2x+2y)

=(x+y)(x−y)−2(x+y)=(x+y)(x-y)-2(x+y)

=(x+y)(x−y−2)

hok tốt nhé

k đi

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

7, \(10ax-5ay-2x+y=5a\left(2x-y\right)-\left(2x-y\right)=\left(5a-1\right)\left(2x-y\right)\)

8, xem lại đề bạn nhé

9, \(4x^2-y^2+8y-16=4x^2-\left(y^2-8y+16\right)=4x^2-\left(y-4\right)^2\)

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

Trả lời:

6, x²y + xy² - 4x - 4y = ( x²y + xy² ) - ( 4x + 4y ) = xy ( x + y ) - 4 ( x + y ) = ( x + y )( xy - 4 )

7, 10ax - 5ay - 2x + y = ( 10ax - 5ay ) - ( 2x - y ) = 5a ( 2x - y ) - ( 2x - y ) = ( 2x - y )( 5a - 1 ) 

8, Sửa đề: x³ - 2x² + 2x - 4 = ( x³ - 2x² ) + ( 2x - 4 ) = x² ( x - 2 ) + 2 ( x - 2 ) = ( x - 2 )( x² + 2 )

9, 4x² - y² + 8y - 16 = 4x² - ( y² - 8y + 16 ) = 4x² - ( y - 4 )² = ( 2x - y + 4 )( 2x + y - 4 )

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(1,a^2-2a+1-b^2\)

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

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

\(=\left(a-1-b\right)\left(a-1+b\right)\)       Khai triển thành hằng đẳng thức số 3 e  nhé.

\(2,x^2+2xy+y^2-81\)

\(=\left(x^2+2xy+y^2\right)-81\)

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

\(=\left(x+y-9\right)\left(x+y+9\right)\)Cái này cũng HĐT số 3 nè

\(3,x^2+6y-9-y^2\)

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

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

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

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

\(5,4x^2+y^2-9-4xy\)

\(=\left(4x^2-4xy+y^2\right)-9\)

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

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

Học tốt