Which of the following expressions are equivalent to 48a^3 - 75a? Select all that apply
A)3(48a^3-75a)
B)3a(16a^2-25)
C)3a(4a+5)(4a+5)
D)3a(4a+5)(4a-5)
E)-3a(25-16a^2)
F)-3a(5-4a)(5+4a)
Show your work
To determine which expressions are equivalent to 48a^3 - 75a, we can factor out the greatest common factor, which is 3a.
48a^3 - 75a = 3a(16a^2 - 25)
Now we can compare the factored expression with the options given:
A) 3(48a^3 - 75a) = 3 * 3a(16a^2 - 25) = 9a(16a^2 - 25) - NOT equivalent
B) 3a(16a^2 - 25) - equivalent
C) 3a(4a+5)(4a+5) = 3a(4a+5)^2 - NOT equivalent
D) 3a(4a+5)(4a-5) - NOT equivalent
E) -3a(25 - 16a^2) = -3a(25 - 4a^2) - NOT equivalent
F) -3a(5 - 4a)(5 + 4a) = 3a(4a - 5)(5 + 4a) - NOT equivalent
Therefore, the expressions that are equivalent to 48a^3 - 75a are B) 3a(16a^2 - 25).