Simplify $m (m^{3} - m^{2} + 1) - 2 (m^{4} - m^{3} - 1) + m^{2} (m^{2} - m + 2)$

2 m^{2} + 5 m + 2

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2 m^{2} + m + 2

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m^{2} + m + 2

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m^{2} + 2 m + 2

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Solution

The correct option is D $2 m^{2} + m + 2$
Given, $m (m^{3} - m^{2} + 1) - 2 (m^{4} - m^{3} - 1) + m^{2} (m^{2} - m + 2)$
$= m^{4} - m^{3} + m - 2 m^{4} + 2 m^{3} + 2 + m^{4} - m^{3} + 2 m^{2}$
$= 2 m^{2} + m + 2$

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Simplify m(m3−m2+1)−2(m4−m3−1)+m2(m2−m+2)

The correct option is D 2m2+m+2Given, m(m3−m2+1)−2(m4−m3−1)+m2(m2−m+2)=m4−m3+m−2m4+2m3+2+m4−m3+2m2=2m2+m+2

Simplify $m (m^{3} - m^{2} + 1) - 2 (m^{4} - m^{3} - 1) + m^{2} (m^{2} - m + 2)$

The correct option is D $2 m^{2} + m + 2$
Given, $m (m^{3} - m^{2} + 1) - 2 (m^{4} - m^{3} - 1) + m^{2} (m^{2} - m + 2)$
$= m^{4} - m^{3} + m - 2 m^{4} + 2 m^{3} + 2 + m^{4} - m^{3} + 2 m^{2}$
$= 2 m^{2} + m + 2$