How do you factor completely #48x^2 + 48xy^2 + 12y^4#?
Step one: Factor out the greatest common factor (which is 12):
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,
b) the middle term is twice the product of the square roots of the first and third terms (in this case
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:
Step three: Putting the 12 in front (that you factored out in the first step) completes the answer: