Answer:
True for all values of a, b and c.
Step-by-step explanation:
(a–3c)(4c+2a)+3c(a+3c)=(2a–c)(3c+5a)–8a^2
Left side:
(a–3c)(4c+2a)+3c(a+3c)
= 4ac + 2a^2 - 12c^2 - 6ac + 3ac + 9c^2
= 2a^2 + ac - 3c^2
Right side:
(2a–c)(3c+5a)–8a^2
= 6ac + 10a^2 - 3c^2 - 5ac - 8a^2
= 2a^2 + ac - 3c^2.
So we see that the left side is identical to the right side so it is true for all values of the variables.
