Question

Answer 1

Câu 1 :

\(A=\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\)

\(\Rightarrow A=\left(a+1\right)\left(a+7\right)\left(a+3\right)\left(a+5\right)+15\)

\(\Rightarrow A=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)

Đặt \(t=a^2+8a+7\)

\(\Rightarrow A=t\left(t+8\right)+15\)

\(\Rightarrow A=t^2+8t+15\)

\(\Rightarrow A=t^2+3t+5t+15\)

\(\Rightarrow A=t\left(t+3\right)+5\left(t+3\right)=\left(t+3\right)\left(t+5\right)\)

\(\Rightarrow A=\left(a^2+8a+7+3\right)\left(a^2+8a+7+5\right)\)

\(\Rightarrow A=\left(a^2+8a+10\right)\left(a^2+8a+12\right)\)