The additive inverse of the polynomial [tex]- 7{y^2} + {x^2}y - 3xy - 7{x^2}[/tex] is [tex]\boxed{7{y^2} - {x^2}y + 3xy + 7{x^2}{\text{ or }} - \left( { - 7{y^2} + {x^2}y - 3xy - 7{x^2}} \right)}.[/tex]
Further explanation:
Given:
The polynomial is [tex]- 7{x^2} + {x^2}y - 3xy - 7{x^2}.[/tex]
Explanation:
The given polynomial is [tex]- 7{y^2} + {x^2}y - 3xy - 7{x^2}.[/tex]
The additive inverse can be defined as when we add a number to some number and get result as zero.
The value of additive inverse is same as of the number but the sign of the additive inverse is opposite.
The additive inverse of the polynomial can be expressed as follows,
[tex]\begin{aligned}A&= - 7{y^2} + {x^2}y - 3xy - 7{x^2} + \left( {7{y^2} - {x^2} + 3xy + 7{x^2}} \right)\\&= - 7{y^2} + 7{y^2} + {x^2}y - {x^2}y - 3xy + 3xy - 7{x^2} + 7{x^2}\\&= 0\\\end{aligned}[/tex]
The additive inverse of the polynomial [tex]- 7{y^2} + {x^2}y - 3xy - 7{x^2}[/tex] is [tex]\boxed{7{y^2} - {x^2}y + 3xy + 7{x^2}{\text{ or }} - \left( { - 7{y^2} + {x^2}y - 3xy - 7{x^2}} \right)}.[/tex]
Learn more:
- Learn more about inverse of the function https://brainly.com/question/1632445.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Polynomial
Keywords: roots, prime polynomial, linear equation, quadratic equation, zeros, function, polynomial, solution, cubic function, degree of the function.
