Factor the following:
3 a^4-75 a^2+432
Factor 3 out of 3 a^4-75 a^2+432:
3 (a^4-25 a^2+144)
a^4-25 a^2+144 = (a^2)^2-25 a^2+144:
3 (a^2)^2-25 a^2+144
The factors of 144 that sum to -25 are -9 and -16. So, (a^2)^2-25 a^2+144 = (a^2-9) (a^2-16):
3 (a^2-9) (a^2-16)
a^2-16 = a^2-4^2:
3 (a^2-9) (a^2-4^2)
Factor the difference of two squares. a^2-4^2 = (a-4) (a+4):
3 (a-4) (a+4) (a^2-9)
a^2-9 = a^2-3^2:
3 (a^2-3^2) (a-4) (a+4)
Factor the difference of two squares. a^2-3^2 = (a-3) (a+3):
Answer: | 3 (a-3) (a+3) (a-4) (a+4)
