\(y^4-8y^2-9\)
\(=\left(y^4-8y^4+16\right)-25\)
\(=\left[\left(y^2\right)^2-2.y^2.4+4^2\right]-5^2\)
\(=\left(y^2-4\right)^2-5^2\)
\(=\left(y^2-4-5\right)\left(y^2-4+5\right)\)
\(=\left(y^2-9\right)\left(y^2+1\right)\)
\(=\left(y-3\right)\left(y+3\right)\left(y^2+1\right)\)
\(y^4-8y^2-9\)
\(=\left(y^4-9y^2\right)+\left(y^2-9\right)\)
\(=\left(y^2-9\right)\left(y^2+1\right)\)
\(=\left(y-3\right)\left(y+3\right)\left(y^2+1\right)\)
Dùng phương pháp tách:
y\(^4\)- 8y\(^2\)- 9
= y\(^4\)+ y\(^2\)-9y\(^2\)- 9
=( y\(^4\) + y\(^2\) ) -( 9y\(^2\)+9)
=y\(^2\)( y\(^2\)+1)- 9(y\(^2\)+1)
= (y\(^2\)-9).(y\(^2\)+1)
=(y-3).(y+3).(y+1)
Đoạn cuối = (y+3)(y-3)(y\(^2\)+1) mới đúng. Mình viết thiếu y\(^2\)
