Answer:
[tex]15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]
Step-by-step explanation:
Given,
Sum of two polynomial = [tex]10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2[/tex]
One addend = [tex]-5a^2b^2 + 12a^2b - 5[/tex]
Let x be the other addend,
[tex]\implies x + (-5a^2b^2 + 12a^2b - 5)=10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2[/tex]
[tex]\implies x = 10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2-(-5a^2b^2 + 12a^2b - 5)[/tex]
[tex]\implies x = 10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2+5a^2b^2 - 12a^2b + 5[/tex]
Combine like terms,
[tex]x=15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]
Hence, other addend is [tex]15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]
