Final answer:
The factors of the quadratic expression 9x^2+24xy+16y^2 are found using the perfect square trinomial method, yielding (3x+4y)(3x+4y) as the correct answer.
Step-by-step explanation:
The correct answer to the question asking for the two binomials that are factors of 9x2+24xy+16y2 is A) (3x+4y)(3x+4y). This can be determined by factoring the quadratic equation using the perfect square trinomial method.
Factoring the quadratic expression requires finding two numbers that multiply to the constant term (16y2) and add up to the middle coefficient (24xy). Recognizing that 9x2 is a perfect square (3x)2 and 16y2 is also a perfect square (4y)2, we look for a binomial squared that matches this pattern. The middle term, 24xy, is twice the product of 3x and 4y, which further indicates that we are dealing with a perfect square trinomial.
The factored form of the quadratic expression is indeed (3x+4y)(3x+4y), as the square of the binomial 3x+4y gives the original trinomial.