factor and simplify 4x^{2}+36x+81
To factor and simplify 4x^2 + 36x + 81, we first notice that all terms are perfect squares.
The trinomial can be rewritten as:
(2x)^2 + 2(2x)(9) + 9^2
Now, we can apply the formula for factoring a perfect square trinomial, which is:
(a + b)^2 = a^2 + 2ab + b^2
In this case, a = 2x and b = 9, so:
(2x + 9)^2
Therefore, the factored and simplified form of 4x^2 + 36x + 81 is (2x + 9)^2.