Answer:
The value of the missing coefficient is 12
Explanation:
* Lets explain how to factorize the difference of two cubes
- The factorization of the difference of two cubes like a³ - b³, is a
product of a binomial and trinomial
- The binomial is the cube root of the first term and the second term
∵ The ∛a³ = a and ∛b³ = b
∴ The binomial is (a - b)
- We will find the trinomial from the binomial by square the 1st term
of the binomial and multiply the 1st term and the 2nd term of the
binomial with opposite sign of the binomial and square the 2nd
term of the binomial
∴ The trinomial is (a² + ab + b²
∴ The factorization of (a³ - b³) is (a - b)(a² + ab + b²)
* Lets solve the problem
∵ 8f³ - 216g³ is the difference of two cubes
∵ ∛(8f³) = 2f
∵ ∛(216g³) = 6g
∴ The binomial is (2f - 6g)
- Lets make the trinomial
∵ (2f)² = 4f²
∵ (2f)(6g) = 12fg
∵ (6g)² = 36g²
∴ The trinomial = (4f² + 12fg + 36g²)
∴ The factorization of 8f³ - 216g³ = (2f - 6g)(4f² + 12fg + 36g²)
∴ The value of the missing coefficient is 12