kindly factor this eq. x16 + 4y32? (treat the numbers after the variable as exponents) thanks so much! ü?
i was given these choices
x8 - 4x4y8 + 2y16
x8 + 2x4y8 + 2y16
x8 - 2x4y8 - 2y16
x8 + 4x4y8 - 2y16
which among these is a factor of the given??helppp
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Verified answer
(x^8)^2 + (2y^16)^2
= (x^8 + 2y^16)^2 - 4x^8y^16
= (x^8 + 2y^16)^2 - (2x^4y^8)^2
..which is a difference of squares, so
= (x^8 + 2y^16 + 2x^4y^8)(x^8 + 2y^16 - 2x^4y^8)
= (x^8 + 2x^4y^8 + 2y^16)(x^8 - 2x^4y^4 + 2y^16)
Your second option is a factor