The sum of $- 5 p q + 5$ , $12 p q + 2$ , $7 p q - 8$ , and $- 2 p q - 5$ is ___________.

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Solution

$(- 5 p q + 5) + (12 p q + 2) + (7 p q - 8) + (- 2 p q - 5)$ $= - 5 p q + 5 + 12 p q + 2 + 7 p q - 8 - 2 p q - 5$
$= (- 5 p q + 12 p q + 7 p q - 2 p q) + (5 + 2 - 8 - 5)$ (Taking the terms having same variables together and constants together)
$= [(- 5 + 12 + 7 - 2) p q] + (5 + 2 - 8 - 5)$ (Coefficients of like terms are added)
$= 12 p q + (- 6)$
$= 12 p q - 6$ .
Therefore, the sum of $- 5 p q + 5$ , $12 p q + 2$ , $7 p q - 8$ , and $- 2 p q - 5$ is $12 p q - 6$ .

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