Question

16. Factor 40y3 - 625

Answer 1

Answer:

Step-by-step explanation:

prime factorization

40y³ = 2³×5y³

625 = 5⁴

Greatest common factor = 5

40y³ - 625 = 5(8y³ - 125)

Note that 8y³ - 125 is the difference of cubes.

8y³ - 125 = (2y)³ - 5³ = (2y-5)((2y)² + 2y·5 + 5²) = (2y-5)(4y² + 10y + 25)

40y³ - 625 = 5(2y-5)(4y² + 10y + 25)