Question

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

Answer 1

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

Explanation:

Given,

Sum of two polynomial =
`10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2`

One addend =
`-5a^2b^2 + 12a^2b - 5`

Let x be the other addend,

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

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

`\implies x = 10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2+5a^2b^2 - 12a^2b + 5`

Combine like terms,

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

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