The addition of the polynomial [tex]x^{3}+3xy-2xy^{2} +y^{3}[/tex] with [tex]2x^{3}-5x^{2} y-3xy^{2}-2y^{3}[/tex] is [tex]3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}[/tex].
What is a polynomial?
⇒ A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
⇒ In the addition of polynomials, the like terms are added while in subtraction, the like terms are subtracted.
Calculation;
We have been given two polynomial which we have to add [tex]x^{3}+3xy-2xy^{2} +y^{3}[/tex] and [tex]2x^{3}-5x^{2} y-3xy^{2}-2y^{3}[/tex]
The sign after addition or subtraction will always be of the variable having more value.
[tex](x^{3}+3xy-2xy^{2} +y^{3} )+(2x^{3}-5x^{2} y-3xy^{2}-2y^{3})[/tex]
On adding like terms with each other
⇒ [tex](x^{3} +2x^{3})+ 3xy-5x^{2} y-(2xy^{2}+3xy^{2})+(y^{3}-2x^{3})[/tex]
⇒ [tex]3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}[/tex]
Hence the addition of the polynomial[tex]x^{3}+3xy-2xy^{2} +y^{3}[/tex] and [tex]2x^{3}-5x^{2} y-3xy^{2}-2y^{3}[/tex] is [tex]3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}[/tex].
Learn more about polynomial here :
brainly.com/question/1487158
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