Write the Following in Expanded Form
\[ (m + 2n – 5p)^2 \]
Solution:
Using identity:
\[ (a+b-c)^2 = a^2+b^2+c^2+2ab-2bc-2ca \]
\[ (m + 2n – 5p)^2 \]
\[ = m^2 + (2n)^2 + (5p)^2 + 2(m)(2n) – 2(2n)(5p) – 2(m)(5p) \]
\[ = m^2 + 4n^2 + 25p^2 + 4mn – 20np – 10mp \]