Answer:
The factor is 11x - 2y ⇒ 2nd answer
Step-by-step explanation:
* Lets explain how to factorize the difference of two cubes
- If we want to factorize x³ - y³
- The binomial x³ - y³ is different of two cubes, because x³ is cube x
and y³ is cube y
- The difference of two cubes has two factors one two two terms and
the other is three terms
- To factorize it we find the ∛x³ and ∛y³
→ ∛x³ = x and ∛y³ = y
→ Then the first factor is (x - y)
→ We find the second factor from the first factor
→ square x
→ square y
→ Multiply x and y and put them between x² and y² with opposite sign
of the first factor
→ The second factor is (x² + xy + y²)
* Lets do the same with 1331x³ - 8y³
∵ [tex]\sqrt[3]{1331x^{3}}=11x[/tex]
∵ [tex]\sqrt[3]{8y^{3}}=2y[/tex]
∴ The first factor is (11x - 2y)
∵ (11x)² = 121x²
∵ (2y)² = 4y²
∵ 11x × 2y = 22xy
∵ The sign of first factor is (-)
∴ The second factor is (121x² + 22xy + 4y²)
∴ The factor is 11x - 2y
