Question

Answer 1

Lời giải:
a.

$x^2-4xy+4y^2-2x+4y-35$
$=(x^2-4xy+4y^2)-2(x-2y)-35$

$=(x-2y)^2-2(x-2y)+1-36=(x-2y-1)^2-6^2=(x-2y-1-6)(x-2y-1+6)$

$=(x-2y-7)(x-2y+5)$

b.

$(x+2)(x+4)(x+6)(x+8)+16$

$=(x+2)(x+8)(x+4)(x+6)+16$

$=(x^2+10x+16)(x^2+10x+24)+16$
$=a(a+8)+16$ (đặt $x^2+10x+16=a$)

$=a^2+8a+16=(a+4)^2=(x^2+10x+20)^2$

Answer 2

`a)x^2 -4xy +4y^2 -2x+4y-35`

`=(x^2 -4xy +4y^2 ) +(-2x+4y)-35`

`=(x-2y)^2 -2(x-2y)-35`

`=(x-2y)^2 -2(x-2y)+1-36`

`=(x-2y-1)^2 -36`

`=[(x-2y-1)-6][(x-2y-1)+6`

`=(x-2y-7)(x-2y+5)`

`b)(x+2)(x+4)(x+6)(x+8)+16`

`=[(x+2)(x+8)][(x+4)(x+6)]+16`

`=(x^2 + 8x+2x+16)(x^2 + 6x+4x+24)+16`

`=(x^2 +10x+16)(x^2 +10x+24)+16`

Đặt `t=x^2 +10x +20`

`=(t-4)(t+4)+16`

`=t^2 -16+16`

`=t^2`

`=(x^2 +10x +20)^2`