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Polynomials — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsPolynomials1 Mark
Question
Multiply the following polynomials.
i. $\left(m^3-2 m+3\right)\left(m^4-2 m^2+3 m+2\right)$
ii. $\left(5 m^3-2\right)\left(m^2-m+3\right)$
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Answer

i. $(m^3 – 2m + 3) (m^4 – 2m^2 + 3m + 2)$
$= m^3(m^4 – 2m^2 + 3m + 2) – 2m(m^4 – 2m^2 + 3m + 2) + 3(m^4 – 2m^2 + 3m + 2)$
$= m^7 – 2m^5 + 3m^4 + 2m^3 – 2m^5 + 4m^3 – 6m^2 – 4m + 3m^4 – 6m^2 + 9m + 6$
$= m^7 – 2m^5 – 2m^5 + 3m^4 + 3m^4 + 2m^3 + 4m^3 – 6m^2 – 6m^2 – 4m + 9m + 6$
$= m^7 – 4m^5 + 6m^4 + 6m^3 – 12m^2 + 5m + 6ii. (5m^3 – 2) (m^2 – m + 3)$
$= 5m^3(m^2 – m + 3) – 2(m^2 – m + 3)$
$= 5m^5 – 5m^4 + 15m^3 – 2m^2 + 2m – 6$

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