Which polynomial can transform $7ab+8b^2+7$ into $9 a^2+ ab + 3$ by only using the addition operator?

Given:

The first polynomial is $7ab+8b^2+7$ and the second polynomial is $9 a^2+ ab + 3$.
To do:

We have to find the polynomial that can transform $7ab+8b^2+7$ into $9 a^2+ ab + 3$ by only using the addition operator.
Solution:
 Let the polynomial that has to be added to $7ab+8b^2+7$ to transform it into $9 a^2+ ab + 3$ be $x$.

This implies,

$(7ab+8b^2+7)+x=9 a^2+ ab + 3$

$x=9a^2+ab+3-(7ab+8b^2+7)$

$x=9a^2-8b^2+ab-7ab+3-7$

$x=9a^2-8b^2-6ab-4$

The required polynomial is $9a^2-8b^2-6ab-4$.

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Updated on: 10-Oct-2022

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