a)x^2-2xy+y^2-m^2+2mn-n^2 phan tich cac du thuc sau thanh nhan tu b) a^2-10a+25-y^2-4yz-4z^2 c) x^2-2x-3 d) a^4+5a^3+15a-9 e) bc ( b+c)+ac (c-a)-ab (a

a)$x^{2}$ – 2xy +$y^{2}$  – $m^{2}$ + 2mn – $n^{2}$

= ($x^{2}$ – 2xy +$y^{2}$) – ( $m^{2}$ – 2mn + $n^{2}$ )
= $(x-y)^{2}$  – $(m-n)^{2}$ 

= ( x – y + m – n ) ( x – y – m + n )

b) $a^{2}$ – 10a + 25 – $y^{2}$ -4yz – $4z^{2}$

= ( $a^{2}$ – 10a + 25 ) – ( $y^{2}$ + 4yz + $4z^{2}$ )

= ( $a^{2}$ – 10a + $5^{2}$ ) – [$y^{2}$ + 4yz + $(2z)^{2}$]

= $(a-5)^{2}$ – $(y+2z)^{2}$

= ( a – 5 + y + 2z ) ( a – 5 – y – 2z )

c) $x^{2}$ – 2x – 3

= $x^{2}$ + x – 3x – 3

= ( $x^{2}$ + x ) – ( 3x + 3 )

= x ( x + 1 ) – 3 ( x + 1 )

= ( x + 1 ) ( x – 3 )

d)$a^{4}$ + $5a^{3}$ + 15a – 9

= $a^{4}$ + $5a^{3}$ – $3a^{2}$ + $3a^{2}$ + 15a – 9

= ( $a^{4}$ + $5a^{3}$ – $3a^{2}$ ) + ( $3a^{2}$ + 15a – 9 )

= $a^{2}$ ( $a^{2}$ + 5a – 3 ) + 3 ( $a^{2}$ + 5a – 3 )

= ( $a^{2}$ + 5a – 3 ) ( $a^{2}$ + 3 )

e) bc ( b + c ) + ac ( c – a )  – ab ( a + b )

= = $b^{2}$c + $bc^{2}$ + $ac^{2}$ – $a^{2}$c – $a^{2}$b – $ab^{2}$ 

g) 4x – 4y + $x^{2}$ – 2xy + $y^{2}$

=( 4x – 4y ) + ( $x^{2}$ – 2xy + $y^{2}$ )

= 4 ( x – y ) + $(x-y)^{2}$

= ( x- y ) ( x – y + 4 )