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 and choose all that apply
To factor out the expression 48a^3 - 75a, we can first look for the greatest common factor (GCF) of both terms:
48a^3 = 3 * 16a^3 = 3 * (4a)^3
75a = 3 * 25a
The GCF is 3a, so we can factor it out:
48a^3 - 75a = 3a(16a^2 - 25)
Now, let's check which expressions are equivalent to 48a^3 - 75a:
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(5 - 4a)(5 + 4a) - Not equivalent
F) -3a(5 - 4a)(5 + 4a) - Not equivalent
Therefore, the expressions that are equivalent to 48a^3 - 75a are:
B) 3a(16a^2 - 25)