Bài 10
a) x^3 + 2x
= x( x^2 + 1)
b) 5(x + 3y) - 15x( x + 3y )
= 5( 1- 3x) ( x + 3y)
c) x^3*y - 2x^2y^2 + 5xy
= xy( x^2 - 2xy + 5)
= xy( x^2 - 2xy + 1 + 4)
= xy*[( x - 1)^2 + 4]
d) 3( x - y) - 5x( y - x)
= 3(x- y) + 5x( x - y)
= (3 + 5x)(x- y)
Bài 11
a) x^2 - 8xy^2 + 16y^4
= x^2 - 2.4xy^2 + (4*y^2)^2
= ( x - 4y^2)
b) ( 5x+ 1)^2 - ( 2xy - 3)^2
= ( 5x + 1 - 2xy + 3 ) ( 5x + 1 + 2xy + 3)
= ( 5x - 2xy + 4) ( 5x + 2xy + 4)
c) 9 - 6x + x^2 - y^2
= ( 3 - x)^2 - y^2
= ( 3 -x - y) ( 3 - x + y)
d) 49( y - 4)^2 - 9( y + 2) ^2
= [ 7( y - 4)]^2 - [ 9(y + 2)]^2
= [ 7( y - 4) - 9( y + 2)]* [ 7( y - 4) + 9( y + 2)]
= (7x - 28 - 9y - 18) * ( 7x - 28 + 9y + 18)
= ( 7x - 9y - 46 ) ( 7x + 9y - 10 )
Bài 12:
a) x^2 - 3x + xy -3y
= (x^2 + xy) - 3( x + y)
= x ( x + y) - 3(x+ y)
= (x - 3)( x + y)
b) 2xy + 3z+ 6y + xz
= 3y( x + 1) + 3z( x + 1)
= 3(y + z) ( x + 1)
c) a^4 - 9a^3 + a^2 - 9a
= (a ^ 4 + a ^2) - 9a( a^2 + 1)
= a^2 ( a^2 + 1) - 9a ( a^2 + 1)
= a( a - 9) ( a^2 + 1)
d) 4x^2 - 4xy + y^2 - 9t^2
= ( 2x - y)^2 - 9t^2
= ( 2x - y - 9t) ( 2x - y + 9t)
e) x^3 - 3x^2 + 3x - 1 - y^3
= ( x - 1)^3 - y^3
= ( x - 1 - y) [( x- 1)^2 + (x -1)*y + y^2]
f) x^2 - 4x^2*y^2 + y^2 + 2xy
= x^2 + 2xy + y^2 - (2xy) ^2
= ( x + y)^2 - (2xy) ^2
= ( x + y - 2xy) ( x + y + 2xy)
