Question

Viết các biểu thức sau thành đa thức:

a) \(\left( {a - 1} \right)\left( {a + 1} \right)\left( {{a^2} + 1} \right)\)                    b) \({\left( {xy + 1} \right)^2} - {\left( {xy - 1} \right)^2}\)

Answer 1

`a, (a-1)(a+1)(a^2+1)`

`= (a^2-1)(a^2+1)`

`= a^4-1`

`b, (xy+1)^2 - (xy-1)^2`

`= x^2y^2 + 2xy + 1 - x^2y^2 + 2xy - 1`

`= 4xy`

Answer 2

a) \(\left(a-1\right)\left(a+1\right)\left(a^2+1\right)\)

\(=\left(a^2-1\right)\left(a^2+1\right)\)

\(=a^4-1\)

b) \(\left(xy+1\right)^2-\left(xy-1\right)^2\)

\(=\left[\left(xy+1\right)-\left(xy-1\right)\right]\left[\left(xy+1\right)+\left(xy-1\right)\right]\)

\(=\left(xy+1-xy+1\right)\left(xy+1+xy-1\right)\)

\(=4xy\)