a) 9x2−6x+1=(3x)2−2.3x.1+129x2−6x+1=(3x)2−2.3x.1+12 =(3x−1)2=(3x−1)2
Hoặc
9x2−6x+1=1−6x+9x29x2−6x+1=1−6x+9x2 =12−2.1.3x+(3x)2=(1−3x)2=12−2.1.3x+(3x)2=(1−3x)2
b) (2x+3y)2+2.(2x+3y)+1(2x+3y)2+2.(2x+3y)+1 =(2x+3y)2+2.(2x+3y).1+12=(2x+3y)2+2.(2x+3y).1+12
Đặt A=2x+3yA=2x+3y; B=1B=1
Khi đó đa thức được viết lại như sau:
(2x+3y)2+2.(2x+3y).1+12(2x+3y)2+2.(2x+3y).1+12 =A2+2AB+B2=(A+B)2=A2+2AB+B2=(A+B)2
Hay:
(2x+3y)2+2.(2x+3y)+1(2x+3y)2+2.(2x+3y)+1
=(2x+3y)2+2.(2x+3y).1+12=(2x+3y)2+2.(2x+3y).1+12
=[(2x+3y)+1]2=(2x+3y+1)2=[(2x+3y)+1]2=(2x+3y+1)2
Đề bài tương tự. Chẳng hạn:
1+2(x+2y)+(x+2y)21+2(x+2y)+(x+2y)2
4x2−12x+94x2−12x+9…