Answer:
[tex]15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]
Step-by-step explanation:
The sum of two polynomials is
[tex]10a^2b^2-8a^2b+6ab^2-4ab+2[/tex]
First addend is
[tex]-5a^2b^2+12a^2b-5[/tex]
Second addend x.
Hence,
[tex]x+(-5a^2b^2+12a^2b-5)=10a^2b^2-8a^2b+6ab^2-4ab+2\\ \\x=10a^2b^2-8a^2b+6ab^2-4ab+2-(-5a^2b^2+12a^2b-5)=\\ \\=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5=\\ \\=(10a^2b^2+5a^2b^2)+(-8a^2b-12a^2b)+6ab^2-4ab+(2+5)=\\ \\=15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]
Answer: The correct option is (A) [tex]15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]
Step-by-step explanation: Given that the sum of two polynomials is [tex](10a^2b^2-8a^2b+6ab^2-4ab+2)[/tex] and one addend is [tex](-5a^2b^2+12a^2b-5).[/tex]
We are to find the other addend.
Let P(x) be the other addend.
Then, according to the given information, we must have
[tex]-5a^2b^2+12a^2b-5+P(x)=10a^2b^2-8a^2b+6ab^2-4ab+2\\\\\Rightarrow P(x)=(10a^2b^2-8a^2b+6ab^2-4ab+2)-(-5a^2b^2+12a^2b-5)\\\\\Rightarrow P(x)=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5\\\\\Rightarrow P(x)=15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]
Thus, the other addend is [tex]15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]
Option (A) is CORRECT.
