Question

Which of the following expressions are equivalent to 48a^3-75a? Select all that apply. Answer 1) 3(48a^3-75a). Answer 2) 3a(16a^2-25) Answer 3)3a(4a+5)(4a+5) Answer 4) 3a(4a+5)(4a-5) Answer 5) -3a(25-16a^2) Answer 6) -3a(5-4a)(5+4a)

Answer 1

The answer is 4) 3a(4a+5)(4a-5)

Answer 2

Answer: The answer is (2), (4), (5) and (6).

Step-by-step explanation: The given expression is

$E=48a^3-75a.$

We are to select the correct expressions from the given options that are equivalent to the above expression.

We have the following forms of the give expressipn:

$E\\\\=48a^3-75a\\\\=3a(16a^2-25)\\\\=3a\left((4a)^2-5^2\right)\\\\=3(4a+5)(4a-5)\\\\=-3a(5+4a)(5-4a)\\\\=-3a(25-16a^2).$

Thus, (2), (4), (5) and (6) are the correct options.