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Fill the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
 3ab-12a+7b+__

 May 6, 2020
 #1
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By Simon's Favorite Factoring Trick, the answer is -56.

 May 7, 2020
 #2
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Fill the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
 3ab-12a+7b+__

 

\(\begin{array}{|rcll|} \hline \mathbf{3ab-12a+7b} &=& 3\left(ab-4a+\dfrac{7}{3}b \right) \\ &=& 3\Bigg( \left(a+\dfrac{7}{3}\right)(b-4)+\dfrac{28}{3} \Bigg) \\ &=& 3\left(a+\dfrac{7}{3}\right)(b-4)+3\cdot \dfrac{28}{3} \\ &=& \left(3a+3\cdot\dfrac{7}{3}\right)(b-4)+3\cdot \dfrac{28}{3} \\ 3ab-12a+7b &=& (3a+7)(b-4)+ 28 \\ \mathbf{3ab-12a+7b-28}&=& \mathbf{(3a+7)(b-4)} \\ \hline \end{array}\)

 

laugh

 May 7, 2020

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