Question

Which of the following expressions are equivalent to 48^3-75a? Select all that apply.
A.) 3(48^3-75a)
B.) 3a(16a^2-25)
C.) 3a(4a+5)(4a+5)
D.)3a(4a+5)(4a-5)
E.)-3a(25-26a^2)
F.) -3a(5-4a)(5+4a)

Answer 1

$48a^3-75a=3a\cdot16a^2-3a\cdot25=\underbrace{3a(16a^2-25)}_{B.)}\\\\=3a\left[(4a)^2-5^2\right]=\underbrace{3a(4a-5)(4a+5)}_{D.)}=\underbrace{-3a(5-4a)(5+4a)}_{F.)}$