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