Question

Find the product:

(x + 5y) (x² – 5xy + 25y²)

Answer 1

Given: (x + 5y)(x² – 5xy + 25y²)

Step-wise calculation:

1. Recognise that this matches the identity of the product of sum and a special trinomial:

(a + b)(a² – ab + b²) = a³ + b³

Here, a = x and b = 5y.

2. Use the identity:

(x + 5y)(x² – 5xy + 25y²) = x³ + (5y)³ 

(x + 5y)(x² – 5xy + 25y²) = x³ + 125y³