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Question
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
Options
x16 − y16
x8 − y8
x8 + y8
x16 + y16
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Solution
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to x8 − y8.
Explanation:
Given `(x-y)(x+y)(x^2 +y^2)(x^4 + y^4)`
Using the identity `(x-y) (x+y) = x^2 - y^2`
`(x-y)(x+y)(x^2 +y^2)(x^4 + y^4) = (x-y)(x+y)(x^2 +y^2)(x^4 + y^4)`
` = (x^2-y^2)(x^2 + y^2)(x^4 + y^4)`
`= [(x^2)^2 - (y^2)^2][x^4 +y^4]`
` = [(x^4)^2 - (y^4)^2]`
` = [x^8 - y^8]`
Hence `(x-y)(x+y)(x^2 +y^2)(x^4 + y^4)` is equal to ` x^8 - y^8`.
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