Question

The sum of two polynomials is 10a2b2 – 8a2b + 6ab2 – 4ab + 2. If one addend is –5a2b2 + 12a2b – 5, what is the other addend?

15a2b2 – 20a2b + 6ab2 – 4ab + 7
5a2b2 – 20a2b2 + 7
5a2b2 + 4a2b2 + 6ab – 4ab – 3
–15a2b2 + 20a2b2 – 6ab + 4ab – 7

Answer 1

Answer: The correct option is (A)
`15a^2b^2-20a^2b+6ab^2-4ab+7.`

Step-by-step explanation: Given that the sum of two polynomials is
`(10a^2b^2-8a^2b+6ab^2-4ab+2)` and one addend is
`(-5a^2b^2+12a^2b-5).`

We are to find the other addend.

Let P(x) be the other addend.

Then, according to the given information, we must have

`-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.`

Thus, the other addend is
`15a^2b^2-20a^2b+6ab^2-4ab+7.`

Option (A) is CORRECT.

Answer 2

`15a^2b^2-20a^2b+6ab^2-4ab+7`

Explanation:

The sum of two polynomials is

`10a^2b^2-8a^2b+6ab^2-4ab+2`

First addend is

`-5a^2b^2+12a^2b-5`

Second addend x.

Hence,

`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`