Question

Simplify: $(a+b+c)(a+b-c)$

Answer 1

Given: $(a+b+c)(a+b-c)$

$$\begin{gathered} (a+b+c)(a+b–c) \\ =(a+b+c)\times (a+b–c) \end{gathered}$$

$$\begin{gathered} =a\times (a+b–c)+b\times (a+b–c)+c\times (a+b–c) \\ =(a\times a)+(a\times b)–(a\times c)+(b\times a)+(b\times b)–(b\times c)+(c\times a)+(c\times b)–(c\times c) \end{gathered}$$

$$\begin{gathered} =a^2+ab–ac+ba+b^2–bc+ca+cb–c^2 \\ =a^2+b^2–c^2+ab+ab–ac+ac–bc+bc \end{gathered}$$

$=a^2+b^2–c^2+2ab$

Hence, the value of $(a+b+c)(a+b-c)$ is $a^2+b^2–c^2+2ab$.