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