Algebra
The product will be reduced 2 times i.e the product will be reduced to half
Step-by-step explanation:
Let the product be [tex]P_{1}[/tex] and the two of its factors are a and b
So [tex]P_{1}[/tex] = [tex]a_{1\\}[/tex]×[tex]b_{1\\}[/tex]
Now if the factor [tex]a_{1\\}[/tex] is increased 3 times, then the new factor will be [tex]a_{2}[/tex]
so [tex]a_{2} = 3a_{1\\}[/tex]
The other factor [tex]b_{1\\}\\[/tex] is decreased 6 times, then the new factor will be [tex]b_{2}[/tex]
so [tex]b_{2 } = \frac{b_{1\\}\\}{6}[/tex]
So the new product [tex]P_{2}[/tex] = [tex]a_{2} b_{2}[/tex]
⇒ [tex]P_{2}\\[/tex] = 3×[tex]a_{1}[/tex]× [tex]\\ \frac{b_{1\\}\\}{6}[/tex]
So [tex]P_{2} = \frac{P_{1}\\}{2}[/tex]
Hence, the product will be reduced 2 times i.e the product will be reduced to half
