Question

1. simplify (m + n)(m² - 2mn + 2n² ).

Explanation:

Step1: Apply distributive property

Multiply \( m \) and \( n \) with each term in the second polynomial:
\( m(m^2 - 2mn + 2n^2) + n(m^2 - 2mn + 2n^2) \)

Step2: Distribute further

For \( m(m^2 - 2mn + 2n^2) \): \( m^3 - 2m^2n + 2mn^2 \)
For \( n(m^2 - 2mn + 2n^2) \): \( m^2n - 2mn^2 + 2n^3 \)

Step3: Combine like terms

Add the two results:
\( m^3 - 2m^2n + 2mn^2 + m^2n - 2mn^2 + 2n^3 \)
Combine \( -2m^2n + m^2n = -m^2n \) and \( 2mn^2 - 2mn^2 = 0 \)
Result: \( m^3 - m^2n + 2n^3 \)

Answer:

\( m^3 - m^2n + 2n^3 \)