Answer:
7(a + 2b)(a² - 2ab + 4b²)
Step-by-step explanation:
Given
7a³ + 56b³ ← factor out 7 from each term
= 7(a³ + 8b³) ← sum of cubes which factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
8b³ = (2b)³ ⇒ b = 2b
a³ + 8b³ = (a + 2b)(a² - 2ab + (2b)²) = (a + 2b)(a² - 2ab + 4b²)
Hence
7a³ + 56b³ = 7(a + 2b)(a² - 2ab + 4b²) ← in factored form
