Write the Following in Expanded Form
\[ (x + 2y + 4z)^2 \]
Solution:
Using identity:
\[ (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \]
\[ (x + 2y + 4z)^2 \]
\[ = x^2 + (2y)^2 + (4z)^2 + 2(x)(2y) + 2(2y)(4z) + 2(4z)(x) \]
\[ = x^2 + 4y^2 + 16z^2 + 4xy + 16yz + 8xz \]