Question

Factor:
50r^8 – 32r^2

The caret symbol represents a power.

2r^2(25r^6+16)=
2r²(25r⁶+16)

DrBob222 forgot a minus sign:

50r^8 – 32r^2 =

2r^2(25r^6 - 16)

Then, inside the brackets, you see a difference of two squares:

25r^6 - 16 = X^2 - Y^2

with X = 5 r^3 and Y = 4

You can then simplify this using

X^2 - Y^2 = (X + Y)(X - Y) --->


25r^6 - 16 = (5 r^3 + 4)(5 r^3 - 4)

You can factor each of these factors further by finding one of the roots.

5 r^3 + 4 = 0 -->

r = -(4/5)^(1/3)

This means that you can divide
5 r^3 + 4 by [r + (4/5)^(1/3)] to obtain a quadratic term. In case of the other factor you find the root
r = (4/5)^(1/3) and you can thus divide the term by [r- (4/5)^(1/3)] to find a quadratic factor.

Thanks to Count Iblis for catching my error. I got so carried away with trying to make the exponents look good that I simply read a minus sign but typed a + sign. Such is old age, bad eyes, and an elevator that doesn't go all the way to the top.