Note that this is the difference of two cubes
Let X = 5a^2; Y = 2b^2
(X - Y)(X^2 + XY - Y^2)
(5a^2 - 2b^2)[25a^4+ (5a^2)(2b^2) + 4b^4]
= (5a^2 - 2b^2)[25a^4 + 10(ab)^2 + 4b^4] <=== Answer
If you want to further factor out 5a^2 - 2b2
Note that 5a^2 - 2b^2 is also the difference of two squares:
= [(a) sqrt(5) + (b) sqrt(2)][(a) sqrt(5) - (b) sqrt(2)][25a^4 + 10(ab)^2 + 4b^4]
(5 a^2-2 b^2) (25 a^4+10 a^2 b^2+4 b^4)
I have no idea how this is achieved, but apparently it's the right answer...
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Verified answer
Note that this is the difference of two cubes
Let X = 5a^2; Y = 2b^2
(X - Y)(X^2 + XY - Y^2)
(5a^2 - 2b^2)[25a^4+ (5a^2)(2b^2) + 4b^4]
= (5a^2 - 2b^2)[25a^4 + 10(ab)^2 + 4b^4] <=== Answer
If you want to further factor out 5a^2 - 2b2
Note that 5a^2 - 2b^2 is also the difference of two squares:
= [(a) sqrt(5) + (b) sqrt(2)][(a) sqrt(5) - (b) sqrt(2)][25a^4 + 10(ab)^2 + 4b^4]
(5 a^2-2 b^2) (25 a^4+10 a^2 b^2+4 b^4)
I have no idea how this is achieved, but apparently it's the right answer...