Question

y^7+y
We are supposed to factor this cube sum. I will give 100 points and brainliest to anybody that answers this with a VERY detailed explanation.

Answer 1

Answer:

• y(y² + 1)(y² - y - 1)(y² + y - 1)

Step-by-step explanation:

• y⁷ + y =
• y(y⁶ + 1) =
• y((y²)³ + 1³) =
• y(y² + 1)(y⁴ - y² + 1) =
• y(y² + 1)(y⁴ - 2y² + 1 - y²) =
• y(y² + 1)((y² - 1)² - y²) =
• y(y² + 1)(y² - y - 1)(y² + y - 1)

Used identities:

• a³ + b³ = (a + b)(a² - ab + b²)
• a² - b² = (a + b)(a - b)
• a² - 2ab + b² = (a - b)²

Answer 2

Algebra

= y⁷ + y

= y(y⁶ + 1³)

= y(y² + 1)(y⁴ - 2y² + 1 - y²)

= y(y² + 1)(y² - y - 1)(y² - y - 1)