Factorization of Polynomials | Factorization of Polynomials Exercise 3F

Question

2𝑎^3 + 16𝑏^3 − 5𝑎 − 10𝑏

Accepted Answer

2𝑎^3 + 16𝑏^3 − 5𝑎 − 10𝑏

= 2(𝑎^3 + 8𝑏^3) − 5(𝑎 + 2𝑏)

According to the equation,

𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)

So we get,

2(𝑎^3 + 8𝑏^3) − 5(𝑎 + 2𝑏)

We can write it as,

= 2(𝑎^3 + (2𝑏)^3) − 5(𝑎 + 2𝑏)

= 2(𝑎 + 2𝑏)(𝑎^2 − 𝑎(2𝑏) + (2𝑏)^2) −5(𝑎 + 2𝑏)

= 2(𝑎 + 2𝑏)(𝑎^2 − 2𝑎𝑏 + 4𝑏^2) − 5(𝑎 + 2𝑏)

By taking (𝑎 + 2𝑏)as common,

We get,

= (𝑎 + 2𝑏)(2(𝑎^2 − 2𝑎𝑏 + 4𝑏^2) − 5)

Question 27