How do you factor #5x ^ { 2} y ^ { 3} + 30x y ^ { 2}# by finding the GCF?

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Answer 1 · 2017-09-03T14:38:08

See a solution process below:

Find the prime factors for each term as:

#5x^2y^3 = 5 xx x xx x xx y xx y xx y#

#30xy^2 = 2 xx 3 xx 5 xx x xx y xx y#

Now identify the common factors and determine the GCF:

#5x^2y^3 = color(red)(5) xx color(red)(x) xx x xx color(red)(y) xx color(red)(y) xx y#

#30xy^2 = 2 xx 3 xx color(red)(5) xx color(red)(x) xx color(red)(y) xx color(red)(y)#

Therefore:

#"GCF" = color(red)(5) xx color(red)(x) xx color(red)(y) xx color(red)(y) = color(red)(5xy^2)#

We can now factor this expression as:

#color(red)(5xy^2)([x xx y] + [2 xx 3]) =>#

#color(red)(5xy^2)(xy + 6)#