Question

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

Answer 1

Option "A"

15a2b2 – 20a2b + 6ab2 – 4ab + 7

hope you pass. <3

Answer 2

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

Explanation:

Let the two polynomial are A and B.

One addend is

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

The sum of two polynomials is

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

Subtract polynomial A from both the sides.

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

`B=10a^2b^2-8a^2b+6ab^2-4ab+2-(-5a^2b^2+12a^2b-5)`

`B=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5`

Combine like terms.

`B=(10a^2b^2+5a^2b^2)+(-8a^2b-12a^2b)+6ab^2-4ab+(2+5)`

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

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