Factorization of Polynomials | Factorization of Polynomials Exercise 3F

Question

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

Accepted Answer

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

8𝑎^3 − 𝑏^3 − 4𝑎𝑥 + 2𝑏𝑥

= (2𝑎)^3 − 𝑏^3 − 2𝑥(2𝑎 − 𝑏)

= (2𝑎 − 𝑏)((2𝑎)^2 + (2𝑎)𝑏 + 𝑏^2) − 2𝑥(2𝑎 − 𝑏)

On further simplification

= (2𝑎 − 𝑏)(4𝑎^2 + 2𝑎𝑏 + 𝑏^2) − 2𝑥(2𝑎 − 𝑏)

= (2𝑎 − 𝑏)(4𝑎^2 + 2𝑎𝑏 + 𝑏^2 − 2𝑥)

Question 24