How do you factor #12a ^ { 2} b - 27b#?

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Answer 1 · 2017-08-08T20:44:42

See a solution process below:

We can factor a #color(red)(3b)# out of each term in the expression:

#(color(red)(3b) * 4a^2) - (color(red)(3b) * 9) =>#

#color(red)(3b)(4a^2 - 9)#

We can then factor the term on the right using this rule:

#color(red)(x)^2 - color(blue)(y)^2 = (color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y))#

#3b(color(red)(4a^2) - color(blue)(9)) =>#

#3b(color(red)(2a) + color(blue)(3))(color(red)(2a) - color(blue)(3))#