Question

[Thị Thu Nguyễn]

Giúp em bài 81 được ko ạ

Answer 1

[Akai Haruma]

81a.

$A=x(x+2)(x+3)(x+5)+9$

$=x(x+5)(x+2)(x+3)+9=(x^2+5x)(x^2+5x+6)+9$

$=(x^2+5x)^2+6(x^2+5x)+9$

$=(x^2+5x+3)^2$

81b.

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

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

$=a(a+8)+16$ (đặt $x^2+10x+16=a$)

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

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

81c.

$C=(x^2+x)^2+9x^2+9x+14=(x^2+x)^2+9(x^2+x)+14$

$=a^2+9a+14$ (đặt $x^2+x=a$)

$=(a^2+7a)+(2a+14)=a(a+7)+2(a+7)$

$=(a+2)(a+7)=(x^2+x+2)(x^2+x+7)$

Answer 2

[Akai Haruma]

81d.

$D=x^2+2xy+y^2+2x+2y-15$

$=(x^2+2xy+y^2)+(2x+2y)-15=(x+y)^2+2(x+y)-15$

$=a^2+2a-15$ (đặt $x+y=a$)

$=(a^2-3a)+(5a-15)=a(a-3)+5(a-3)=(a-3)(a+5)$

$=(x+y-3)(x+y+5)$

81e.

$E=x^2-2xy+y^2+2x-2y-3=(x^2-2xy+y^2)+(2x-2y)-3$

$=(x-y)^2+2(x-y)-3=a^2+2a-3$ (đặt $x-y=a$)

$=(a^2-a)+(3a-3)=a(a-1)+3(a-1)=(a+3)(a-1)$

$=(x-y+3)(x-y-1)$

81g.

$G=(x^2+x)^2+5y(x^2+x)+6y^2$

$=(x^2+x)^2+2y(x^2+x)+3y(x^2+x)+6y^2$

$=(x^2+x)(x^2+x+2y)+3y(x^2+x+2y)$

$=(x^2+x+2y)(x^2+x+3y)$

81h.

$H=(x^2-x+1)(x^2+3x+1)+4x^2$
$=(a-x)(a+3x)+4x^2$ (đặt $x^2+1=a$)

$=a^2+2ax+x^2=(a+x)^2=(x^2+1+x)^2$