Question

625x^4 - 64y^8

Answer 1

the hint to this problem is that these two terms are suspiciously using perfect squares,

Answer 2

so you use the idea of "difference of squares"

\[(a+b)(a-b) = a^2 -b^2\]

Answer 3

\[625x^4 = (25x)^2\]

and

\[64y^4 = (8y^4)^2\]

Answer 4

so you can factor this as

\[(25x^2-8y^4)(25x^2+8y^4)\]

Answer 5

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

\[(5x-2\sqrt{2}y^2)(5x+2\sqrt{2}y^2)\]

Answer 6

are you good ?

Answer 7

yes! thank you so mich