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Question
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Solution
We have,
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
`=> x(x^2 - 3x - 1)(x^2 - 3x + 1)`
`=>x[[x^2 - 3x]^2 - [1]^2]` `[∵ (a - b)(a +b^2) = a^2 - b^2]`
`=> x[(x^2)^2 + (-3x)^2 - 2(+3x)x^2] - 1]`
`=> x[x^4 + 9x^2 - 6x^3 - 1]`
`=> x^5 - 6x^4 + 9x^3 - x`
`∴ (x^3 - 3x^2 - 2)(x^2 - 3x + 1) = x^5 - 6x^4 + 9x^3 - x`
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