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

Answer:

a=$5q^ {2}$

b=$r^{2}s$

Step-by-step explanation:

Here $125q^{6}$ is like the $a^{3}$ in the general formula.

So we can write $125q^{6}$ as:

$(5q^ {2} )^{3}$

We can also write $r^{6} s^{3}$ as:

$(r^{2}s)^{2}$

Therefore:

a³=$(5q^ {2} )^{3}$

b²=$(r^{2}s)^{2}$

Answer 2

Answer:

a = 5q²

b = r²s

Step-by-step 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.