đề sai nha bạn
mình sửa đề cho:
\(A=\left(x+1\right)\left(x+2\right)\left(x+7\right)\left(x+8\right)+8\)
\(A=\left(x+1\right)\left(x+8\right)\left(x+2\right)\left(x+7\right)+8\)
\(A=\left(x^2+9x+8\right)\left(x^2+9x+14\right)+8\)
Đặt \(x^2+9x+8=a\)
\(\Rightarrow A=a\left(a+6\right)+8=a^2+6a+8=\left(a+2\right)\left(a+4\right)\)
\(\Rightarrow A=\left(x^2+9x+8+2\right)\left(x^2+9x+8+4\right)=\left(x^2+9x+10\right)\left(x^2+9x+12\right)\)
Mình nghĩ là bạn sai đề rồi.Mình có cách làm khác:
(x+1)(x+2)(x+7)(x+8)+8
=((x+1)(x+8))((x+2)(x+7))+8
=(x^2+9x+8)(x^2+9x+14)+8
=(x^2+9x+11-3)(x^2+9x+11+3)+8
=(x^2+9x+11)-9+8=(x^2+9x+11-1)(x^2+9x+11+1)
=(x^2+9x+10)(x^2+9x+12).
