Question

Which of the following is a factor of 1331x3 − 8y3?

4
11x − 2y
121x2 + 44xy + 4y2
121x2 − 22xy + 4y2

Answer 1

Answer: 11x - 2y

Proof of validity is hsown below.

Answer 2

The factor is 11x - 2y ⇒ 2nd answer

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

∵
`\sqrt[3]{1331x^(3)}=11x`

∵
`\sqrt[3]{8y^(3)}=2y`

∴ 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