Write the Following in Expanded Form
\[ (-2x + 3y + 2z)^2 \]
Solution:
Using identity:
\[ (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \]
\[ (-2x + 3y + 2z)^2 \]
\[ = (-2x)^2 + (3y)^2 + (2z)^2 + 2(-2x)(3y) + 2(3y)(2z) + 2(2z)(-2x) \]
\[ = 4x^2 + 9y^2 + 4z^2 – 12xy + 12yz – 8xz \]