Question

How can I resolve this expression with polynomials?

Answer 1

(m^2 + m + 1)(m + 1) + (m^2 - m - 1)(m - 1) - 2m(m^2 + 1)

= m^3 + m^2 + m^2 + m + m + 1 + (m^2 - m - 1)(m - 1) - 2m(m^2 + 1)

= m^3 + 2m^2 + 2m + 1 + (m^2 - m - 1)(m - 1) - 2m(m^2 + 1)

= m^3 + 2m^2 + 2m + 1 + m^3 - m^2 - m^2 + m - m + 1 - 2m(m^2 + 1)

= 2m^3 + 2m + 2 - 2m(m^2 + 1)

= 2m^3 + 2m + 2 - 2m^3 - 2m

= 2

Answer 2

2

Explanation:

Expand the first and second pair of factors by multiplying each term in the first factor by each term in the second factor. Distribute the third factor by - 2m

(m² + m + 1)(m + 1) + (m² - m - 1)(m - 1) - 2m(m² + 1)

= m³ + m² + m + m² + m + 1 + m³ - m² - m - m² + m + 1 - 2m³ - 2m

Collect like terms

= (m³ + m³ - 2m³) + (m² + m² - m² - m²) + (m + m - m + m - 2m) + (1 + 1)

= 0 + 0 + 0 + 2

= 2