Question

expand the following (4a-2b+3c)^2​

Answer 1

$\mathbb{\bold{\underline{ANSWER}}}$

$\fbox{\textsf{16a ^{\textsf{2}} + 4b ^{\textsf{2}} + 9c ^{\textsf{2}} -16ab -12bc + 24ac}}$

$\mathbb{\bold{\underline{EXPLANATION:}}}$

$\star \textsf{ Expression Given : \textbf{(4a - 2b + 3c) ^{\textbf{2}} }}$

$\star \to \textsf{(4a - 2b + 3c) ^{\textsf{2}} = [4a + (-2b) + 3c] ^{\textsf{2}} }$

  $\bullet \textbf{ Using the identity: (a + b + c) ^{\textbf{2}} = a ^{\textbf{2}} + b ^{\textbf{2}} + c ^{\textbf{2}} + 2ab + 2bc + 2ca}$$\star \texttt{ a = 4a}$

$\star \texttt{ b = -2b}$

$\star \texttt{ c = 3c}$

$\textsf{Substituting the values in a ^{\textsf{2}} + b ^{\textsf{2}} + c ^{\textsf{2}} + 2ab + 2bc + 2ca, we get :}}$

$\star \to \textsf{[(4a) ^{\textsf{2}} + (-2b) ^{\textsf{2}} + (3c) ^{\textsf{2}} + (2 x 4a x -2b) + (2 x -2b x 3c) + (2 x 3c x 4a)] }$

$\to \textsf{16a ^{\textsf{2}} + 4b ^{\textsf{2}} + 9c ^{\textsf{2}} + (-16ab) + (-12bc) + (24ac)}$

$\textsf{= 16a ^{\textsf{2}} + 4b ^{\textsf{2}} + 9c ^{\textsf{2}} -16ab -12bc + 24ac}$

$\therefore \textbf{(4a - 2b + 3c) ^{\textbf{2}} = 16a ^{\textsf{2}} + 4b ^{\textsf{2}} + 9c ^{\textsf{2}} -16ab -12bc + 24ac}$