Question

Factorise a²b − b³. Using this result, find the value of 101² × 100 − 100³.

Answer 1

a²b − b³

b(a² − b²)

b(a + b) (a − b)

Now, 

101² × 100 − 100³

= 100 (1012 − 100²)

= 100 (101 + 100) (101 − 100)

= 100 (201) (1)

= 20100