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Question
Simplify the following products:
`(2x^4 - 4x^2 + 1)(2x^4 - 4x^2 - 1)`
Solution
We have
`[2x^2 - 4x^2 + 1][2x^4 - 4x^2 - 1]`
`=> [(2x^4 - 4x^2)^2 - (1)^2] [∵ (a + b)(a - b) = a^2 - b^2]`
`=> [(2x^4)^2 + (4x^2)^2 - 2(2x^4)(4x^2) - 1]`
`=> 4x^8 + 16^4 - 16x^6 - 1 [∵ (a - b)^2 = a^2 + b^2 - 2ab]`
`=> 4x^8 - 16x^6 + 16x^4 - 1`
`∴ [2x^4 - 4x^2 + 1][2x^4 - 4x^2 - 1] = 4x^8 - 16x^6 + 16x^4 - 1`
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