625x^4 - 64y^8

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625x^4 - 64y^8

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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the hint to this problem is that these two terms are suspiciously using perfect squares,
so you use the idea of "difference of squares" \[(a+b)(a-b) = a^2 -b^2\]
\[625x^4 = (25x)^2\] and \[64y^4 = (8y^4)^2\]

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so you can factor this as \[(25x^2-8y^4)(25x^2+8y^4)\]
the left part of the factors are again, difference of squares, so you can use the idea again to get something the only thing here is that 8 is not a perfect square anymore, so you can either leave it like this or factor even further like \[(5x-2\sqrt{2}y^2)(5x+2\sqrt{2}y^2)\]
are you good ?
yes! thank you so mich

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