Question

Factor completely and then place the factors in the proper location on the grid.

81a2 + 36a + 4

Answer 1

what's 81a2?

Answer 2

81a^2

Answer 3

(9x+2)(9x+2)

Answer 4

highest power is 2, so your going to have (a + ?)(a + ?). you have 81a^2, so the first two multiply to get 81. Probably\[(9a + ?)(9a + ?)\] but it doesnt have to be. you know they are both plus because when you multiply out \[? \times ? = 4\] which is positive. The second term is 36a so\[9a \times ? + 9a \times ? = 36a\] = 36a factoring out the ? gives\[?(9a + 9a) = 36a = ?(18a)\]
solving for ? gives \[? = \frac{36a}{18a} = 2\]

so \[81a^{2} + 36a + 4 = (9a +2)(9a + 2)\]

the hard bit is really guessing what the coefficient of a is. I guessed 9 which turns out to be correct.