An additive inverse of a polynomial is a number or expression that, when added to the original polynomial, results in a sum of 0. It is also known as the opposite of the polynomial. In other words, the negative of a polynomial is its additive inverse. In mathematics, polynomials are the expressions that use positive and negative exponents, and variables multiplied together. Therefore, the additive inverse of the polynomial -7y2+x2y-3xy-7×2 is the number or expression that when added to the original polynomial will result in a sum of 0.
The Formula for Calculating the Additive Inverse of a Polynomial
The formula for calculating the additive inverse of a polynomial is quite simple and involves the use of the distributive property. The distributive property is used to break down a polynomial into its individual components. Once the individual components have been identified, the additive inverse can be calculated by multiplying each component by -1. For example, if the polynomial is -7y2+x2y-3xy-7×2, the additive inverse can be calculated by multiplying each component by -1: ( -7y2*-1) + ( x2y*-1) – ( 3xy*-1) – ( 7×2*-1). This yields 7y2-x2y+3xy+7×2, which is the additive inverse of the original polynomial.
Example of Using the Formula to Calculate the Additive Inverse of a Polynomial
Let’s look at an example to better understand how to use the formula to calculate the additive inverse of a polynomial. Consider the polynomial -5×2+3xy-2y2-3×3. To calculate the additive inverse, we need to multiply each component by -1: (-5×2*-1) + (3xy*-1) – (2y2*-1) – (3×3*-1). This yields 5×2-3xy+2y2+3×3, which is the additive inverse of the original polynomial.
Conclusion
In conclusion, the additive inverse of a polynomial is a number or expression that, when added to the original polynomial, will result in a sum of 0. The formula for calculating the additive inverse of a polynomial involves the use of the distributive property, which is used to break down a polynomial into its individual components. Once the individual components have been identified, the additive inverse can be calculated by multiplying each component by -1. This article provides an example of how to use the formula to calculate the additive inverse of a polynomial.
This article discussed what is the additive inverse of the polynomial -7y2+x2y-3xy-7×2. It explained the formula for calculating the additive inverse of a polynomial and provided an example of how to use the formula to find the additive inverse of a polynomial. Finally, it summarized the key points of the article.
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