Question

x3 –x2y – xy2 – y3 and x3 – 2x 2y + 3xy2 + 4y

Answer 1

1 ans (x-y) ²(x+y)

2ans (x-2y) (x²+3y²(/

Answer 2

Note: The question requires finding the addition of the given terms.

Given,

$\[{f_1}\left( x \right) = {x^3} - {x^2}y - x{y^2} - {y^3}\]$

$\[{f_2}\left( x \right) = {x^3} - 2{x^2}y + 3x{y^2} + 4y\]$

Solution,

Add the given terms.

$\[\begin{array}{l} \Rightarrow \left( {{x^3} - {x^2}y - x{y^2} - {y^3}} \right) + \left( {{x^3} - 2{x^2}y + 3x{y^2} + 4y} \right)\\ \Rightarrow \left( {{x^3} + {x^3}} \right) + \left( { - {x^2}y - 2{x^2}y} \right) + \left( { - x{y^2} + 3x{y^2}} \right) + \left( { - {y^3}} \right) + \left( {4y} \right)\\ \Rightarrow 2{x^3} - 3{x^2}y + 2x{y^2} - {y^3} + 4y\end{array}\]$

Hence, the required addition of the terms is $\[2{x^3} - 3{x^2}y + 2x{y^2} - {y^3} + 4y.\]$