Answer:
c×3 (2 b^3 - 2 a b + a)
Step-by-step explanation:
Simplify the following:
c (4 b^3 + 3 a) + b (2 c b^2 - 6 a c)
Hint: | Factor common terms out of 2 c b^2 - 6 a c.
Factor 2 c out of 2 c b^2 - 6 a c:
c (4 b^3 + 3 a) + b×2 c (b^2 - 3 a)
Hint: | Pull a common factor out of c (4 b^3 + 3 a) + b×2 c (b^2 - 3 a).
Factor c out of c (4 b^3 + 3 a) + b×2 c (b^2 - 3 a), resulting in c ((4 b^3 + 3 a) + b×2 (b^2 - 3 a)):
c (4 b^3 + 3 a + 2 b (b^2 - 3 a))
Hint: | Distribute 2 b over b^2 - 3 a.
2 b (b^2 - 3 a) = 2 b^3 - 6 a b:
c (4 b^3 + 3 a + 2 b^3 - 6 a b)
Hint: | Group like terms in 4 b^3 + 3 a - 6 a b + 2 b^3.
Grouping like terms, 4 b^3 + 3 a - 6 a b + 2 b^3 = (4 b^3 + 2 b^3) - 6 a b + 3 a:
c (4 b^3 + 2 b^3) - 6 a b + 3 a
Hint: | Add like terms in 4 b^3 + 2 b^3.
4 b^3 + 2 b^3 = 6 b^3:
c (6 b^3 - 6 a b + 3 a)
Hint: | Factor out the greatest common divisor of the coefficients of 6 b^3 - 6 a b + 3 a.
Factor 3 out of 6 b^3 - 6 a b + 3 a:
Answer: c×3 (2 b^3 - 2 a b + a)
