The other polynomial addend, when the sum of two polynomials is 10a2b2 – 8a2b 6ab2 – 4ab is 15a²b²- 20a²b + 6ab² - 4ab + 7.
<h3>What is polynomial?</h3>
Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
The sum of two polynomials is,
![10a^2b^2 - 8a^2b+ 6ab^2 - 4ab+2](https://tex.z-dn.net/?f=10a%5E2b%5E2%20-%208a%5E2b%2B%206ab%5E2%20-%204ab%2B2)
The one polynomial addend is,
![-5a^2b^2 +12a^2b - 5](https://tex.z-dn.net/?f=-5a%5E2b%5E2%20%2B12a%5E2b%20-%205)
Let suppose the other polynomial addend is f(a,b). Thus,
![(-5a^2b^2 +12a^2b - 5)+f(a,b)=(10a^2b^2 - 8a^2b+ 6ab^2 - 4ab+2)](https://tex.z-dn.net/?f=%28-5a%5E2b%5E2%20%2B12a%5E2b%20-%205%29%2Bf%28a%2Cb%29%3D%2810a%5E2b%5E2%20-%208a%5E2b%2B%206ab%5E2%20-%204ab%2B2%29)
Isolate the second polynomial as,
![f(a,b)=(10a^2b^2 - 8a^2b+ 6ab^2 - 4ab+2)-(-5a^2b^2 +12a^2b - 5)\\f(a,b)=10a^2b^2 - 8a^2b+ 6ab^2 - 4ab+2+5a^2b^2 -12a^2b + 5](https://tex.z-dn.net/?f=f%28a%2Cb%29%3D%2810a%5E2b%5E2%20-%208a%5E2b%2B%206ab%5E2%20-%204ab%2B2%29-%28-5a%5E2b%5E2%20%2B12a%5E2b%20-%205%29%5C%5Cf%28a%2Cb%29%3D10a%5E2b%5E2%20-%208a%5E2b%2B%206ab%5E2%20-%204ab%2B2%2B5a%5E2b%5E2%20-12a%5E2b%20%2B%205)
Arrange the like terms as,
![f(a,b)=10a^2b^2+5a^2b^2 - 8a^2b -12a^2b+ 6ab^2 - 4ab + 2+5\\f(a,b)=15a^2b^2- 20a^2b + 6ab^2 - 4ab + 7](https://tex.z-dn.net/?f=f%28a%2Cb%29%3D10a%5E2b%5E2%2B5a%5E2b%5E2%20-%208a%5E2b%20-12a%5E2b%2B%206ab%5E2%20-%204ab%20%2B%202%2B5%5C%5Cf%28a%2Cb%29%3D15a%5E2b%5E2-%2020a%5E2b%20%2B%206ab%5E2%20-%204ab%20%2B%207)
Hence, the other polynomial addend, when the sum of two polynomials is 10a2b2 – 8a2b 6ab2 – 4ab is 15a²b²- 20a²b + 6ab² - 4ab + 7.
Learn more about polynomial here;
brainly.com/question/24380382