Mathematics 2022 JAMB Past Questions - Question 6: Factorise completely 8p + 125py³

Correct Answer

B

Explanation

To factorize completely the expression 8p + 125py³, we can look for common factors among the terms. In this case, the common factor is 1p, which we can factor out:8p + 125py³ = p(8 + 125y³)Now, we can see that the expression inside the parentheses, 8 + 125y³, is the sum of cubes. We can use the formula for the sum of cubes, which states that a³ + b³ = (a + b)(a² - ab + b²).In this case, a = 2 and b = 5y:8 + 125y³ = (2)³ + (5y)³          = (2 + 5y)(4 - 10y + 25y²)Therefore, the completely factorized form of 8p + 125py³ is:8p + 125py³ = p(2 + 5y)(4 - 10y + 25y²)