\(A=\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\)
\(=\left[\left(a+1\right)\left(a+7\right)\right]\left[\left(a+3\right)\left(a+5\right)\right]+15\)
\(=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)
Đặt : \(a^2+8+11=t\) khi đó pt trở thành :
\(\left(t-4\right)\left(t+4\right)+15=t^2-16+15=t^2-1=\left(t-1\right)\left(t+1\right)\)
\(=\left(a^2+8a+11-1\right)\left(a^2+8a+11+1\right)\)
\(=\left(a^2+8a+10\right)\left(a^2+8a+12\right)\)
\(=\left(a+2\right)\left(a+6\right)\left(a^2+8a+10\right)\)
Chúc bạn học tốt !!!
A = (a+1)(a+3)(a+5)(a+7) + 15
A = [ (a+1) (a+7)] [(a+3) (a+5)] + 15
A= ( a2 + 8a + 7)( a2 + 8a + 15 ) + 15 (*)
Đặt a2 + 8a + 7 = t
=> A = t.(t+8) + 15
A = t2 + 8t + 15
A = t2 + 3t + 5t + 15
A = ( t +3).(t+5)
Thay A = ( t +3).(t+5) vào (*)
=> A = ( a2 + 8a + 7 + 3).( a2 + 8a + 7 + 5)
A = ( a2 + 8a + 10).( a2 + 8a + 12 )
A = ( a2 + 8a + 10).( a2 + 6a + 2a + 12 )
A = ( a2 + 8a + 10) ( a+6)(a+2)
a=(a+1)(a+3)(a+5)(a+7)+15
a=[ (a+1)(a+7) ] [(a+3)(a+5)] +15
a=(a²+8a+7)(a²+8a+15)+15
Đặt a²+8a+7=t
a=t.(t+8)+15
a=t²+8t+15
a=t²+3t+5t+15
a=(t+3).(t+5)
Hok tok