Question

Use the identity below to complete the tasks:

a3 - b3 = (a - b)(a + ab + b2)
When using the identity for the sum of two cubes
to factor 125q6-r6s3.
What is a?
What is b?
DONE

Answer 1

a = 5r² and b = r²s

Explanation:

a3 - b3 = (a - b)(a + ab + b2)

Expressing 125q^6-r^6s^3 as a difference of 2 cubes

125q^6-r^6s^3

= 5³(r²)³ - (r³)²s³

= (5r²)³ - (r²s)³

Comparing with a³ - b³

a = 5r² and b = r²s

Hence the value of a is 5r² and b is r²s