Final answer:
The expression 9a⁴ + 12a²b² + 4b⁴ is equivalent to option A, which is (3a² + 2b²)², a perfect square trinomial.
Step-by-step explanation:
The expression 9a⁴ + 12a²b² + 4b⁴ is a perfect square trinomial and can be rewritten as a square of a binomial. To determine which of the given options is equivalent, we look for a binomial squared that gives us the original expression when expanded.
Option A, (3a² + 2b²)², when expanded (using FOIL or the binomial theorem), results in 9a⁴ + 12a²b² + 4b⁴, which is our original expression. Therefore, this is the correct choice.
The other options do not match the original expression when expanded. Options B, C, and D are incorrect because they would either result in exponents that are too high (B and D) or coefficients that do not match (C).
Complete Question:
9a⁴ + 12a²b² + 4b⁴
Which of the following is equivalent to the expression shown above?
A (3a² + 2b²)²
B (3a + 2b)⁴
C (9a² + 4b²)²
D (9a + 4b)⁴