Check if the following equality is true for all values of variables: (a-3c) (4c+2a) + 3c (a+3c) = (2a-c) (3c+5a) - 8a^2

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.