Question

Tính tổng và hiệu của hai đa thức sau:

E = \(5xy-\dfrac{2}{3}x^2y+xyz^2-1\) và F = \(2x^2y-xyz^2-\dfrac{2}{5}xy+x+\dfrac{1}{2}\)

Giúp mk nha các bn, mk cần gấp lắm!

Answer 1

E + F = (5xy - \(\dfrac{2}{3}\)x\(^2\)y + xyz\(^2\) - 1) + (2x\(^2\)y - xyz\(^2\) - \(\dfrac{2}{5}\)xy + x + \(\dfrac{1}{2}\))

= 5xy - \(\dfrac{2}{3}\)x\(^2\)y + xyz\(^2\) - 1 + 2x\(^2\)y -xyz\(^2\) - \(\dfrac{2}{5}\)xy + x + \(\dfrac{1}{2}\)

= (5xy - \(\dfrac{2}{5}\)xy) + (\(\dfrac{-2}{3}\)x\(^2\)y + 2x\(^2\)y) + (xyz\(^2\) - xyz\(^2\)) + (-1 + \(\dfrac{1}{2}\)) + x

= \(\dfrac{23}{5}\)xy + \(\dfrac{4}{3}\) x\(^2\)y - \(\dfrac{1}{2}\) + x

Answer 2

E - F = (5xy - \(\dfrac{2}{3}\)x\(^2\)y + xyz\(^2\) - 1) - (2x\(^2\)y - xyz\(^2\) - \(\dfrac{2}{5}\)xy + x + \(\dfrac{1}{2}\))

= 5xy - \(\dfrac{2}{3}\)x\(^2\)y + xyz\(^2\) - 1 - 2x\(^2\)y + xyz\(^2\) + \(\dfrac{2}{5}\)xy - x - \(\dfrac{1}{2}\)

= (5xy + \(\dfrac{2}{5}\)xy) + (\(\dfrac{-2}{3}\)x\(^2\)y - 2x\(^2\)y) + (xyz\(^2\) + xyz\(^2\))+ (-1 - \(\dfrac{1}{2}\)) - x

= \(\dfrac{27}{5}\)xy - \(\dfrac{8}{3}\)x\(^2\)y + 2xyz\(^2\) - \(\dfrac{3}{2}\) - x

Vậy E - F = \(\dfrac{27}{5}\)xy - \(\dfrac{8}{3}\)x\(^2\)y + 2xyz\(^2\) - \(\dfrac{3}{2}\) - x

Answer 3

\(\left\{{}\begin{matrix}E=5xy-\dfrac{2}{3}x^2y+xyz^2-1\left(1\right)\\F=\dfrac{-2}{5}xy-2x^2y-2xyz^2+x+\dfrac{1}{2}\left(2\right)\end{matrix}\right.\)

Tính tổng --> (1)+(2)

\(E+F=\left(5-\dfrac{2}{5}\right)xy+\left(-\dfrac{2}{3}-2\right)x^2y+\left(1-2\right)xyz^2+\left(0+1\right)x+\left(-1+\dfrac{1}{2}\right)\)rút gọn

\(E+F=\dfrac{23}{5}xy-\dfrac{8}{3}x^2y-1xyz^2+x+\dfrac{1}{2}\)

Tính hiệu Lấy (1) trừ (2)

\(E-F=\dfrac{27}{5}xy+\dfrac{4}{3}x^2y+3xyz^2-x-\dfrac{3}{2}\)