Question

Tính tổng của hai đa thức sau :

a) \(5x^2y-5xy^2+xy\) và \(xy-x^2y^2+5xy^2\)

b) \(x^2+y^2+z^2\) và \(x^2-y^2+z^2\)

Answer 1

a) (5x²y-5xy²+xy) + (xy-x²y²+5xy²)

= 5x²y-5xy²+xy+xy-x²y²+5xy²

= 5x²y+(5xy²-5xy²)+(xy+xy)-x²y²

= 5x²y+2xy-x²y²

b) (x²+y²+z²) + (x²-y²+z²)

= x²+y²+z²+x²-y²+z²

= (x²+x²)+(y²-y²)+(z²+z²)

= 2x²+2z²

Answer 2

a)( \(5x^2y\)\(-\) \(5xy^2\) \(+\) \(xy\)) + (\(xy\) \(-\) \(x^2y^2\) \(+\) \(5xy^2\))

= \(5x^2y-5xy^2+xy+xy-x^2y^2+5xy^2\)

= \(5x^2y+2xy-x^2y^2\)

b) \(\left(x^2+y^2+z^2\right)+\left(x^2-y^2+z^2\right)\)

= \(x^2+y^2+z^2+x^2-y^2+z^2\)

=\(2x^2+2z^2\)

=\(2\left(x+z\right)^2\)