Explain the procedures used for factoring perfect squares. Include 2 examples.
Check if the middle term can be expressed as 2(square root of first term)(square root of second term).
If yes, then it is a perfect square. You just take (square root of first term +/- square root of second term)^2 as your answer.
\(\quad a^2 + 4ab + 4b^2\\ = a^2 + 2(a)(2b) + (2b)^2\\ = (a + 2b)^2\)
\(\quad x^2 - 6xy + 9y^2\\ = x^2 -2(x)(3y) + (3y)^2\\ = (x - 3y)^2\).