Question

PHÂN TÍCH:

a) \(\left(x+2\right)\left(x-4\right)\left(x+6\right)\left(x-12\right)+36x^2\)

b) \(4\left(x+5\right)\left(x+6\right)\left(x+10\right)\left(x+12\right)-3x^2\)

c) \(\left(x-18\right)\left(x-7\right)\left(x+35\right)\left(x+90\right)-67x^2\)

Answer 1

Làm 1 câu các câu còn lại tương tự!

a, \(\left(x+2\right)\left(x-4\right)\left(x+6\right)\left(x-12\right)+36x^2\)

\(=\left[\left(x+2\right)\left(x-12\right)\right]\left[\left(x-4\right)\left(x+6\right)\right]+36x^2\)

\(=\left(x^2-12x+2x-24\right)\left(x^2+6x-4x-24\right)+36x^2\)

\(=\left(x^2-10x-24\right)\left(x^2+2x-24\right)+36x^2\)(1)

Đặt \(a=x^2-10x-24\Rightarrow a+12x=x^2+2x-24\)

\(\Rightarrow\left(1\right)=a\left(a+12x\right)+36x^2=a^2+12ax+36x^2\)

\(=a^2+6ax+6ax+36x^2=a\left(a+6x\right)+6x\left(a+6x\right)\)

\(=\left(a+6x\right)^2\)(*)

Vì \(a=x^2-10x-24\) nên

(*)\(=\left(x^2-10x-24+6x\right)^2=\left(x^2-4x-24\right)^2\)

Vậy...........