Question

Use the identity below to complete the tasks: a3 − b3 = (a − b)(a2 + ab + b2) When using the identity for the sum of two cubes to factor 125q6 − r6s3. What is a? What is b?

Answer 1

What is a? ✔ 5q² (which is the first choice)

What is b? ✔ r²s (which is the last choice)

Factor the expression:

(5q^2-r^2s) (25q^4+ 5q^2r^2s+ 1r^4s^2)

The answer of the numbers are in bold for the factor expression

Explanation:

Answer 2

a = 5q²

b = r²s

Explanation:

The given identity is
`a^(3)-b^(3)=(a-b)(a^(2)+ab+b^(2))`

we have to use this identity to factor of two cubes given as
`[tex]125q^(6)-r^(6)s^(3)=(5q^(2))^(3)-(r^(2)s)^(3)`[/tex]

As this expression is in the form of a³- b³

Here a is 5q² and b is r²s.