Question

Factor Completely: 81a2 + 36a + 4

Answer 1

Look at the expression and find that the leading term and the constant term are both perfect squares. We find what the middle term needs to be for this to be a perfect square, keeping in mind that \[(a+b)^2=a^2+2ab+b^2\]and sure enough, it is. That means\[81a^2 + 36a + 4=(9a)^2+2(9a)(2)+2^2=(9a+2)^2\]

Answer 2

Edit (last line of text before the last equation): it is a perfect square.