Đáp án:
Tham khảo
Giải thích các bước giải:
$ 1)[(x+2)(x+4)][(x+6)(x+8)]+16$
$=(x²+10+16x)(x²+10x+24)+16$
$=(x²+10+20-4)(x²+10+20+4)+16$
$=(x²+10+20)²-16+16$
$=(x²+10+20)²$
2)
$[(x+2)(x+3)][(x+4)(x+5)]-24$
$=(x²+7x+10)(x²+7x+12)-24$
$Đặt x²+7x+10=y,ta có:$
$y²+2y-24=(y-4)(y+6)$
$=(x²+7x+6)(x²+7x+16)$
$=(x+1)(x+6)(x²+7x+16)$
$3)x(x+4)(x+6)(x+10)+128$
$=(x²+10x)(x²+10x+24)+128$
$=(x²+10x+12-12)(x²+10x+12+12)+128$
$=(x²+10x+12)²-144+128$
=$(x²+10+12)²-16$
$=(x²+10x+12-4)(x²+10+12+4)$
$=(x²+10+8)(x²+10x+16)$
$=(x²+10+8)(x+2)(x+8)$
