How do you factor completely #48x^2 + 48xy^2 + 12y^4#?

1 Answer
Jan 6, 2016

Answer:

#12(2x+y^2)^2#

Explanation:

Step one: Factor out the greatest common factor (which is 12):
#12(4x^2+4xy^2 + y^4)#

Step two: Recognize that this is a perfect square. Remember that Perfect Square Trinomials have:
a) first and last terms that are positive perfect squares (in this case, #4x^2# and #y^4#.
AND
b) the middle term is twice the product of the square roots of the first and third terms (in this case #2xy^2 xx 2 = 4xy^2#

When you have a perfect square, you can factor it by taking the square root of the first and last terms, putting them inside a bracket, and squaring the bracket:

#(2x+y^2)^2#

Step three: Putting the 12 in front (that you factored out in the first step) completes the answer:
#12(2x+y^2)^2#