Question

Add the following polynomial of x3+3xy-2×y2+y3,2×3-5x2y-3xy2-2y3​

Answer 1

The addition of the polynomial $x^{3}+3xy-2xy^{2} +y^{3}$ with $2x^{3}-5x^{2} y-3xy^{2}-2y^{3}$ is  $3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}$.

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   $x^{3}+3xy-2xy^{2} +y^{3}$ and $2x^{3}-5x^{2} y-3xy^{2}-2y^{3}$

The sign after addition or subtraction will always be of the variable having more value.

$(x^{3}+3xy-2xy^{2} +y^{3} )+(2x^{3}-5x^{2} y-3xy^{2}-2y^{3})$

On adding like terms with each other

⇒ $(x^{3} +2x^{3})+ 3xy-5x^{2} y-(2xy^{2}+3xy^{2})+(y^{3}-2x^{3})$

⇒ $3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}$

Hence the addition of the polynomial$x^{3}+3xy-2xy^{2} +y^{3}$ and $2x^{3}-5x^{2} y-3xy^{2}-2y^{3}$ is $3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}$.

Learn more about polynomial here :

brainly.com/question/1487158

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