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Question
Multiply the following polynomial.
`(m^3 - 2m + 3)(m^4 - 2m^2 + 3m + 2)`
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Solution
`(m^3 - 2m + 3)(m^4 - 2m^2 + 3m + 2)`
`= m^3 (m^4 - 2m^2 + 3m + 2) - 2m (m^4 - 2m^2 + 3m + 2) + 3(m^4 - 2m^2 + 3m + 2)` ...(Each term of second polynomials is multiplied by each term of first polynomial.)
`= m^7 - 2m^5 + 3m^4 + 2m^3 -2m^5 + 4m^3 - 6m^2 - 4m + 3m^4 - 6m^2 + 9m + 6`
`= m^7 - 2m^5 - 2m^5 + 3m^4 + 3m^4 +2m^3 +4m^3 - 6m^2 - 6m^2 - 4m + 9m + 6` ...(Like terms taken together.)
`= m^7 - 4m^5 + 6m^4 + 6m^3 - 12m^2 + 5m +6`
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