Question

6. Simplify:
(i) (a + b + c)^2 + (a - b + c)^2​

Answer 1

Answer

Apply the formula a

2

−b

2

=(a+b)(a−b) to simplify the given expression.

(a+b+c)

2

−(a−b+c)

2

=(a+b+c+a−b+c){a+b+c−(a−b+c)}

=(2a+2c)(a+b+c−a+b−c)

=(2a+2c)(2b)

=4ab+4bc

Answer 2

Answer:-

$\\ \tt\hookrightarrow (a + b + c) {}^{2} + (a - b + c {)}^{2} \\ \\ \tt\hookrightarrow {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca + {a}^{2} + {b}^{2} + {c}^{2} - 2ab - 2bc + 2ca \\ \\ \tt\hookrightarrow {a}^{2} + {a}^{2} + {b}^{2} + {b}^{2} + {c}^{2} + {c}^{2} + 2ab - 2ab + 2bc - 2bc + 2ca + 2ca \\ \\ \tt\hookrightarrow 2 {a}^{2} + {2b}^{2} + {2c}^{2} + 0 + 0 + 4ca \\ \\ \tt\hookrightarrow {2a}^{2} + {2b}^{2} + {2c}^{2} + 4ca \\ \\ \tt\hookrightarrow 2( {a}^{2} + {b}^{2} + {c }^{2} + 2ca)$