Question

Hi I need help with this question please and thank you

Answer 1

Expression given:

$64t^3+125v^6$

Factoring:

0. Applying the Law of exponents

$64t^3+125v^6=\mleft(4t\mright)^3+\mleft(5v^2\mright)^3$

2. D = Sum of Cubes:

$=(4t)^3+(5v^2)^3=(4t+5v^2)((4t)^2-4t\cdot\: 5v^2+(5v^2)^2)$

Simplifying:

$=\mleft(4t+5v^2\mright)\mleft(16t^2-20tv^2+25v^4\mright)$

Then, the only Factoring Pattern we need is D.

Answer: D.