Question

factor $324x^{2} + 972x + 729$ using the perfect square trinomial method (if applicable).
a. not a perfect square trinomial
b. $(18x - 27)^{2}$
c. $18x(x + 54)$
d. $(18x + 27)^{2}$

Explanation:

Step1: Identify square terms

First term: $\sqrt{324x^2}=18x$, last term: $\sqrt{729}=27$

Step2: Verify middle term

Check $2\times18x\times27=972x$, matches given middle term.

Step3: Write perfect square form

Since all conditions are met, the trinomial is $(18x+27)^2$

Answer:

d. $(18x + 27)^2$